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diff --git a/modal-analysis/index.org b/modal-analysis/index.org
index f68e0a4..923dff9 100644
--- a/modal-analysis/index.org
+++ b/modal-analysis/index.org
@@ -20,7 +20,31 @@
#+HTML_MATHJAX: align: center tagside: right font: TeX
:END:
-The modal analysis of the ID31 Micro-station consists of several parts:
+The goal is to experimentally extract a *Spatial Model* (mass, damping, stiffness) of the structure (shown on figure [[fig:nass_picture]]) in order to tune the Multi-Body model.
+
+#+name: fig:nass_picture
+#+caption: Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass
+#+attr_html: :width 500px
+[[file:img/nass_picture.png]]
+
+The procedure is represented on figure [[fig:vibration_analysis_procedure]] where we go from left to right.
+
+#+name: fig:vibration_analysis_procedure
+#+caption: Vibration Analysis Procedure
+#+attr_html: :width 400px
+[[file:img/vibration_analysis_procedure.png]]
+
+The steps are:
+- we obtain a *Response Model* (Frequency Response Functions) from measurements (described [[file:measurement.org][here]])
+- the response model is further converted into a *Modal Model* (Natural Frequencies and Mode Shapes) (described [[file:modal_extraction.org][here]])
+- this is converted into a *Spatial Model* with the Mass/Damping/Stiffness matrices (described [[file:mathematical_model.org][here]])
+
+Theses matrices will be used to tune the Simscape (multi-body) model.
+
+The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
+
+
+The modal analysis of the ID31 Micro-station thus consists of several parts:
- [[file:measurement.org][Frequency Response Measurements]]
- [[file:modal_extraction.org][Modal Parameter Extraction]]
- [[file:mathematical_model.org][Derivation of Mathematical Model]]
diff --git a/modal-analysis/mat/acc_pos.txt b/modal-analysis/mat/acc_pos.txt
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index 0000000..0fa610c
--- /dev/null
+++ b/modal-analysis/mat/acc_pos.txt
@@ -0,0 +1,23 @@
+ 23 1.5500e-001 -9.0000e-002 -5.9400e-001
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+ 20 8.6490e-001 -5.0600e-001 -9.5060e-001
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+ 9 -4.7500e-001 -4.1400e-001 -4.2730e-001
+ 8 3.8000e-001 -3.0000e-001 -4.1680e-001
+ 7 4.2000e-001 2.8000e-001 -4.1680e-001
+ 6 -4.2000e-001 2.8000e-001 -4.1680e-001
+ 5 -3.8500e-001 -3.0000e-001 -4.1680e-001
+ 4 6.4000e-002 -6.4000e-002 -2.9600e-001
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diff --git a/modal-analysis/mat/frf_coh_matrices.mat b/modal-analysis/mat/frf_coh_matrices.mat
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diff --git a/modal-analysis/mat/id31_nanostation.cfg b/modal-analysis/mat/id31_nanostation.cfg
new file mode 100644
index 0000000..7194774
--- /dev/null
+++ b/modal-analysis/mat/id31_nanostation.cfg
@@ -0,0 +1,90 @@
+This file was saved by N-Modal automatically.
+16:49:47, Monday, July 01, 2019
+
+HEADER
+Data are imported from UFF files.
+
+
+FREQVEC
+UFF
+
+RES_TYPE
+ACCELERATION
+
+COOR_SYS
+ 1 0 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 Cartesian1
+
+NODES
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+SETUP
+Setup 1
+FILE
+C:\Users\lesourd\Downloads\id31_modal_analysis\uff_data\Measurement1.uff|Measurement2.uff|Measurement3.uff|Measurement4.uff|Measurement5.uff|Measurement6.uff|Measurement7.uff|Measurement8.uff|Measurement9.uff|Measurement10.uff|Measurement11.uff|Measurement12.uff|Measurement13.uff|Measurement14.uff|Measurement15.uff|Measurement16.uff|Measurement17.uff|Measurement18.uff|Measurement19.uff|Measurement20.uff|Measurement21.uff|Measurement22.uff|Measurement23.uff|Measurement24.uff
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+ 17Z+: 1.42791e-001 1.41492e-001
+ 18X-: 2.38478e-003 2.01321e-002
+ 18Y-: 5.57283e-002 5.57094e-002
+ 18Z+: -6.95583e-003 1.88998e-002
+ 19X-: 1.24551e-002 1.50428e-002
+ 19Y-: 4.53742e-002 4.24108e-002
+ 19Z+: -1.56612e-001 -1.52638e-001
+ 20X-: 3.41276e-002 3.62056e-002
+ 20Y-: 6.06514e-002 4.21505e-002
+ 20Z+: 6.68460e-002 1.17220e-001
+ 21X-: -3.75561e-002 3.37291e-002
+ 21Y-: 1.46833e-003 -8.38924e-002
+ 21Z+: 2.25130e-002 -1.56436e-002
+ 22X-: -1.02525e-002 4.87003e-002
+ 22Y-: -1.96867e-002 -8.21470e-002
+ 22Z+: 1.68703e-002 -6.27926e-002
+ 23X-: -3.89762e-002 4.44931e-002
+ 23Z+: 8.51820e-003 -7.14570e-003
+ 23Y+: 1.92463e-002 7.79396e-002
+ 1X-: 3.50861e-002 -2.19931e-002
+ 1Y-: -7.16977e-002 -2.04598e-002
+ 1Z+: 2.92012e-002 -1.25382e-002
+ 2X-: 3.19810e-002 -1.43584e-002
+ 2Y-: -8.00415e-002 -2.25942e-002
+ 2Z+: 5.63089e-002 6.06573e-003
+ 3Y-: -7.26208e-002 -2.13908e-002
+ 3X+: -4.29234e-002 6.98265e-003
+ 3Z+: 4.75277e-002 2.62996e-002
+ 4X-: 3.40086e-002 -2.24185e-002
+ 4Y-: -5.70973e-002 -1.29427e-002
+ 4Z+: 1.61911e-002 4.98311e-003
+ 5X-: -1.84045e-002 -3.79862e-002
+ 5Y-: 1.34920e-002 -2.13017e-001
+ 5Z+: -8.56236e-003 -3.10474e-002
+ 6X-: -1.28128e-002 -1.47459e-002
+ 6Y-: 5.50841e-002 1.21362e-002
+ 6Z+: 9.51668e-002 2.81070e-003
+ 7X-: -4.44054e-002 -4.02699e-002
+ 7Y-: 5.55706e-002 -2.09976e-004
+ 7Z+: 1.91526e-002 2.45270e-002
+ 8X-: 1.28732e-003 1.23168e-002
+ 8Y-: 8.37346e-002 3.99176e-002
+ 8Z+: -3.23238e-002 2.40723e-002
+ 9X-: -2.17623e-002 -1.77784e-002
+ 9Y-: 3.00754e-002 2.70035e-002
+ 9Z+: -4.11723e-002 1.48332e-002
+ 10X-: 7.11608e-002 9.83590e-003
+ 10Y-: 3.99240e-001 6.35974e-002
+ 10Z+: 3.25644e-001 3.90991e-002
+ 11X-: -2.34831e-002 9.25893e-003
+ 11Y-: 4.56240e-001 7.80094e-002
+ 11Z+: 4.81365e-001 0.00000e+000
+ 12X-: 6.92362e-003 -1.21448e-002
+ 12Y-: 1.19187e-001 5.12997e-002
+ 12Z+: -3.12677e-002 -1.40030e-002
+ 13X-: 3.25489e-002 1.88661e-002
+ 13Y-: 1.48974e-002 1.36472e-002
+ 13Z+: 6.21421e-002 5.78920e-002
+ 14X-: 1.96402e-003 1.05830e-002
+ 14Y-: 4.87782e-003 1.25245e-002
+ 14Z+: -3.97379e-002 -2.53172e-002
+ 15X-: 1.23055e-002 1.01995e-002
+ 15Y-: 2.96664e-003 1.58193e-002
+ 15Z+: -7.07192e-002 -5.80739e-002
+ 16X-: -2.47336e-003 1.41266e-002
+ 16Y-: 1.77344e-003 2.77450e-002
+ 16Z+: 6.16527e-002 7.91265e-002
+ 17X-: 1.52142e-002 2.27048e-002
+ 17Y-: 2.56495e-002 2.88367e-002
+ 17Z+: 9.02655e-002 1.06442e-001
+ 18X-: 1.47944e-002 1.75665e-002
+ 18Y-: 3.67090e-002 4.39057e-002
+ 18Z+: -6.64044e-002 -4.85581e-002
+ 19X-: 6.54482e-003 9.72706e-003
+ 19Y-: 2.83197e-002 4.87456e-002
+ 19Z+: -1.16460e-001 -1.38545e-001
+ 20X-: 1.27102e-002 2.25280e-002
+ 20Y-: 2.12515e-002 3.73299e-002
+ 20Z+: 6.11394e-002 6.56215e-002
+ 21X-: -2.34249e-003 -2.68757e-002
+ 21Y-: 5.40329e-002 3.22775e-002
+ 21Z+: 4.07525e-002 1.08185e-002
+ 22X-: -1.88091e-002 -4.26278e-002
+ 22Y-: 6.10286e-002 3.63879e-002
+ 22Z+: 8.43691e-002 5.31388e-002
+ 23X-: -6.61190e-003 -3.26827e-002
+ 23Z+: 1.62616e-002 1.18004e-002
+ 23Y+: -5.82587e-002 -3.37040e-002
diff --git a/modal-analysis/mat/modes.asc b/modal-analysis/mat/modes.asc
new file mode 100644
index 0000000..6742dae
--- /dev/null
+++ b/modal-analysis/mat/modes.asc
@@ -0,0 +1,1600 @@
+Created by N-Modal
+Estimator: bbfd
+01-Jul-19 16:44:11
+
+
+Mode 1
+freq = 11.41275Hz
+damp = 8.72664%
+modal A = -4.50556e+003-9.41744e+003i
+modal B = -7.00928e+005+2.62922e+005i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: -1.04114e-001 3.50664e-002
+ 1Y-: 2.34008e-001 5.04273e-004
+ 1Z+: -1.93303e-002 5.08614e-003
+ 2X-: -8.38439e-002 3.45978e-002
+ 2Y-: 2.42440e-001 0.00000e+000
+ 2Z+: -7.40734e-003 5.17734e-003
+ 3Y-: 2.17655e-001 6.10802e-003
+ 3X+: 1.18685e-001 -3.54602e-002
+ 3Z+: -2.37725e-002 -1.61649e-003
+ 4X-: -1.13539e-001 2.12740e-002
+ 4Y-: 2.29591e-001 2.29845e-002
+ 4Z+: -2.85848e-002 -1.90513e-003
+ 5X-: -9.92321e-002 2.68214e-002
+ 5Y-: 2.11882e-001 2.12300e-002
+ 5Z+: -1.95505e-002 2.19196e-002
+ 6X-: -9.01605e-002 2.86991e-002
+ 6Y-: 2.21620e-001 2.01387e-002
+ 6Z+: 4.30911e-002 1.58030e-002
+ 7X-: -8.74840e-002 3.24811e-002
+ 7Y-: 2.04432e-001 1.46592e-002
+ 7Z+: -1.53182e-002 -2.29349e-002
+ 8X-: -9.64016e-002 2.26978e-002
+ 8Y-: 2.06812e-001 1.24367e-002
+ 8Z+: -7.78993e-002 -1.94759e-002
+ 9X-: -8.04992e-002 5.11235e-003
+ 9Y-: 2.18565e-001 2.17642e-002
+ 9Z+: -1.85553e-002 3.30641e-003
+ 10X-: -8.15750e-002 1.75855e-002
+ 10Y-: 2.33588e-001 -1.28464e-002
+ 10Z+: 8.25770e-002 -1.80163e-002
+ 11X-: -8.61128e-002 1.48094e-002
+ 11Y-: 2.16915e-001 -1.75267e-002
+ 11Z+: -7.84767e-003 -1.73285e-003
+ 12X-: -9.15311e-002 1.21702e-002
+ 12Y-: 2.11104e-001 -2.76812e-002
+ 12Z+: -1.27430e-001 1.05756e-002
+ 13X-: -4.53037e-002 6.50677e-003
+ 13Y-: 5.32168e-002 -1.38055e-002
+ 13Z+: -4.28407e-002 4.07865e-003
+ 14X-: -4.09512e-002 7.04588e-003
+ 14Y-: 5.45171e-002 -1.34153e-002
+ 14Z+: 1.02197e-001 -2.51682e-002
+ 15X-: -4.38899e-002 8.89008e-003
+ 15Y-: 5.39942e-002 -1.00846e-002
+ 15Z+: 6.36132e-003 -1.60326e-003
+ 16X-: -4.45647e-002 1.90226e-002
+ 16Y-: 5.19365e-002 7.39449e-003
+ 16Z+: -1.07008e-001 3.70171e-002
+ 17X-: -2.81833e-002 5.89670e-003
+ 17Y-: 3.14956e-002 -4.21112e-003
+ 17Z+: -7.99339e-003 2.09140e-003
+ 18X-: -3.14771e-002 3.58104e-003
+ 18Y-: 2.91201e-002 -5.82573e-003
+ 18Z+: 1.56823e-001 -2.66584e-002
+ 19X-: -2.75551e-002 5.15899e-003
+ 19Y-: 3.20351e-002 -2.55580e-003
+ 19Z+: -4.13937e-003 2.69403e-003
+ 20X-: -2.98064e-002 5.38356e-003
+ 20Y-: 3.50555e-002 -1.22429e-003
+ 20Z+: -1.71853e-001 2.27513e-002
+ 21X-: -9.14183e-002 4.39931e-002
+ 21Y-: 2.03922e-001 8.54607e-003
+ 21Z+: -1.64797e-002 1.06766e-002
+ 22X-: -1.08925e-001 3.80720e-002
+ 22Y-: 1.88674e-001 1.20327e-002
+ 22Z+: 3.84435e-003 -2.14475e-003
+ 23X-: -1.01160e-001 4.18162e-002
+ 23Z+: -3.44999e-002 -7.29388e-003
+ 23Y+: -1.83573e-001 -1.87552e-002
+
+Mode 2
+freq = 18.51409Hz
+damp = 11.75321%
+modal A = -1.56119e+003-1.64408e+004i
+modal B = -1.92061e+006-4.44325e+004i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 1.39073e-001 -5.17657e-002
+ 1Y-: 1.45371e-001 -1.43499e-002
+ 1Z+: 2.11993e-002 -1.05691e-002
+ 2X-: 1.42040e-001 -5.55098e-002
+ 2Y-: 1.38246e-001 -8.52685e-003
+ 2Z+: -6.15322e-003 -1.39585e-002
+ 3Y-: 1.62248e-001 -1.57330e-002
+ 3X+: -1.22695e-001 5.00805e-002
+ 3Z+: 1.36569e-002 1.48713e-002
+ 4X-: 1.43704e-001 -4.42894e-002
+ 4Y-: 1.36816e-001 -8.32750e-003
+ 4Z+: 3.43340e-002 2.73575e-002
+ 5X-: 1.25675e-001 -7.41651e-002
+ 5Y-: 1.56470e-001 -2.93481e-002
+ 5Z+: 1.34641e-002 -6.06536e-002
+ 6X-: 1.06587e-001 -7.49628e-002
+ 6Y-: 1.44955e-001 -1.44595e-002
+ 6Z+: -7.56815e-002 -9.99131e-002
+ 7X-: 1.08635e-001 -6.96294e-002
+ 7Y-: 1.70413e-001 -1.92324e-002
+ 7Z+: 2.13882e-002 9.07495e-002
+ 8X-: 1.28358e-001 -8.09426e-002
+ 8Y-: 1.79260e-001 -1.84480e-002
+ 8Z+: 1.17080e-001 1.01100e-001
+ 9X-: 1.23209e-001 2.69807e-003
+ 9Y-: 1.48080e-001 -1.18281e-002
+ 9Z+: 1.02918e-002 1.01579e-002
+ 10X-: 1.01099e-001 -6.45456e-003
+ 10Y-: 1.86020e-001 4.70512e-003
+ 10Z+: -9.54427e-002 -2.75079e-003
+ 11X-: 1.06267e-001 -1.21937e-002
+ 11Y-: 2.21606e-001 -3.46945e-018
+ 11Z+: 3.49920e-002 -1.19491e-002
+ 12X-: 1.38357e-001 -2.36532e-002
+ 12Y-: 2.01405e-001 -5.82074e-003
+ 12Z+: 1.75597e-001 -1.22658e-002
+ 13X-: 5.78053e-002 -3.99595e-003
+ 13Y-: -5.39127e-002 -8.25407e-003
+ 13Z+: 5.17746e-002 -4.03076e-003
+ 14X-: 5.04828e-002 -5.90168e-004
+ 14Y-: -5.51983e-002 -6.30961e-003
+ 14Z+: -1.14840e-001 -1.12504e-002
+ 15X-: 5.37827e-002 1.91645e-003
+ 15Y-: -5.85920e-002 -1.37577e-003
+ 15Z+: -4.75312e-003 -3.36771e-004
+ 16X-: 4.26944e-002 1.52218e-002
+ 16Y-: -7.70123e-002 1.38594e-002
+ 16Z+: 1.02101e-001 3.43183e-002
+ 17X-: 3.40887e-002 1.47930e-003
+ 17Y-: -3.39844e-002 -1.86788e-003
+ 17Z+: 3.72057e-003 1.17791e-003
+ 18X-: 4.01731e-002 -1.34539e-003
+ 18Y-: -2.85419e-002 -3.22209e-003
+ 18Z+: -1.87675e-001 -1.39181e-002
+ 19X-: 3.31431e-002 4.08475e-003
+ 19Y-: -3.45880e-002 -1.91397e-003
+ 19Z+: 7.62434e-003 5.62444e-003
+ 20X-: 3.58788e-002 3.59223e-003
+ 20Y-: -4.13673e-002 -4.57835e-004
+ 20Z+: 2.04494e-001 2.13871e-002
+ 21X-: 9.53764e-002 -1.24983e-001
+ 21Y-: 1.94099e-001 -8.41872e-005
+ 21Z+: 1.10398e-002 -2.50765e-002
+ 22X-: 6.70823e-002 -1.36280e-001
+ 22Y-: 2.03021e-001 -1.01055e-002
+ 22Z+: -1.34242e-002 -1.28208e-003
+ 23X-: 9.33021e-002 -1.32599e-001
+ 23Z+: 5.89230e-002 3.64352e-002
+ 23Y+: -2.03632e-001 5.95685e-004
+
+Mode 3
+freq = 37.58431Hz
+damp = 6.44322%
+modal A = 1.24918e+004-2.00022e+004i
+modal B = -4.52363e+006-3.24813e+006i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 1.67804e-001 -5.03747e-002
+ 1Y-: -1.83896e-002 8.32516e-002
+ 1Z+: -5.43020e-002 -2.09562e-002
+ 2X-: 1.58437e-001 4.13117e-002
+ 2Y-: -2.58681e-002 8.81354e-002
+ 2Z+: -3.94928e-002 -2.08294e-002
+ 3Y-: 7.85127e-003 3.34137e-003
+ 3X+: -1.65124e-001 -3.40186e-002
+ 3Z+: -3.45808e-004 1.48630e-003
+ 4X-: 1.67903e-001 -4.75348e-002
+ 4Y-: -8.10166e-003 3.42447e-003
+ 4Z+: -1.10244e-002 7.43494e-003
+ 5X-: 2.73736e-001 1.38778e-017
+ 5Y-: -1.68148e-001 -3.48924e-002
+ 5Z+: -1.31297e-001 -5.75910e-002
+ 6X-: -5.13323e-002 -5.68501e-002
+ 6Y-: -2.69651e-001 -8.09149e-003
+ 6Z+: -1.11644e-001 -6.18222e-002
+ 7X-: -4.65391e-002 -4.99712e-002
+ 7Y-: 2.14271e-001 6.64604e-002
+ 7Z+: 1.05217e-001 5.89110e-002
+ 8X-: 2.41334e-001 -8.83008e-003
+ 8Y-: 2.14149e-001 6.96147e-002
+ 8Z+: 3.79366e-002 3.76814e-002
+ 9X-: 2.68325e-001 4.06674e-002
+ 9Y-: -2.63785e-001 -9.78269e-003
+ 9Z+: -1.85744e-001 -3.77166e-002
+ 10X-: -9.43498e-003 -1.73976e-002
+ 10Y-: -2.36651e-001 -2.07240e-002
+ 10Z+: 5.93900e-003 9.26713e-003
+ 11X-: -2.89998e-002 -3.24830e-002
+ 11Y-: 2.14362e-001 7.74264e-002
+ 11Z+: -2.65907e-004 -1.78472e-002
+ 12X-: 2.62486e-001 2.88100e-002
+ 12Y-: 1.78001e-001 5.92939e-002
+ 12Z+: 9.69885e-002 -2.18624e-002
+ 13X-: 2.05032e-002 -3.42483e-003
+ 13Y-: -2.70762e-003 -1.89782e-003
+ 13Z+: -1.55118e-002 -1.82971e-002
+ 14X-: -8.26340e-003 -7.40611e-003
+ 14Y-: -2.85678e-003 -1.47995e-004
+ 14Z+: 4.55236e-003 2.63915e-003
+ 15X-: -6.39431e-003 -4.79397e-003
+ 15Y-: 1.02974e-002 1.18643e-002
+ 15Z+: 1.58412e-003 1.27396e-003
+ 16X-: 2.69059e-002 2.32923e-002
+ 16Y-: 2.60867e-002 4.42990e-002
+ 16Z+: 1.22151e-002 2.64957e-002
+ 17X-: 1.03689e-002 1.84941e-003
+ 17Y-: -2.78169e-003 3.24662e-003
+ 17Z+: -3.58237e-003 -3.04469e-003
+ 18X-: -9.11671e-003 -9.65962e-003
+ 18Y-: -7.88115e-003 -4.95051e-004
+ 18Z+: 1.58301e-002 2.09768e-002
+ 19X-: -6.48845e-003 -1.94827e-003
+ 19Y-: 1.39840e-002 1.10725e-002
+ 19Z+: 1.62973e-003 8.15455e-003
+ 20X-: 1.12034e-002 2.70859e-003
+ 20Y-: 1.57573e-002 1.48056e-002
+ 20Z+: -1.16338e-002 -2.17142e-002
+ 21X-: 6.25582e-002 -9.71540e-002
+ 21Y-: -4.21302e-002 1.05387e-001
+ 21Z+: -5.52408e-002 -3.00149e-002
+ 22X-: 3.32372e-002 1.03164e-002
+ 22Y-: -2.20490e-002 4.17948e-002
+ 22Z+: -1.22529e-002 -5.06289e-003
+ 23X-: 5.84987e-002 -9.24191e-002
+ 23Z+: 3.97339e-003 3.78159e-003
+ 23Y+: -5.16890e-003 3.00456e-002
+
+Mode 4
+freq = 39.43487Hz
+damp = 3.60695%
+modal A = -1.83730e+004+8.73583e+004i
+modal B = 2.14671e+007+5.33018e+006i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: -9.14037e-002 -8.35958e-002
+ 1Y-: -6.00469e-003 3.30675e-002
+ 1Z+: 3.55898e-002 -6.86058e-003
+ 2X-: -9.10675e-002 -7.11987e-002
+ 2Y-: 8.61991e-003 4.51691e-002
+ 2Z+: 2.91774e-002 -6.70216e-003
+ 3Y-: -1.61510e-002 1.70407e-002
+ 3X+: 8.72622e-002 7.06259e-002
+ 3Z+: 1.21259e-002 -5.24675e-003
+ 4X-: -1.00974e-001 -1.15038e-001
+ 4Y-: -6.28304e-003 4.81907e-002
+ 4Z+: 2.21535e-002 9.18535e-003
+ 5X-: -1.37653e-001 -1.42624e-001
+ 5Y-: 3.64227e-001 0.00000e+000
+ 5Z+: 1.18133e-001 2.00150e-003
+ 6X-: 3.02737e-002 -6.22754e-002
+ 6Y-: 1.50042e-001 1.04531e-001
+ 6Z+: 5.18741e-002 -6.05851e-003
+ 7X-: 5.25967e-002 -5.36685e-002
+ 7Y-: -1.26825e-001 -3.07164e-002
+ 7Z+: -6.54468e-002 1.68347e-002
+ 8X-: -2.01475e-001 -1.40757e-001
+ 8Y-: -1.58889e-001 -2.47575e-002
+ 8Z+: -4.31233e-002 2.28669e-003
+ 9X-: -1.69264e-001 -1.02709e-001
+ 9Y-: 1.89283e-001 1.02689e-001
+ 9Z+: 1.38244e-001 4.05092e-002
+ 10X-: 8.26234e-003 -3.14862e-002
+ 10Y-: 2.58006e-001 1.14415e-001
+ 10Z+: -1.74463e-002 2.00714e-002
+ 11X-: -1.85420e-003 -4.31495e-002
+ 11Y-: -2.04818e-001 -9.17264e-002
+ 11Z+: -7.77154e-003 -3.94052e-002
+ 12X-: -2.84217e-001 -1.93841e-001
+ 12Y-: -2.16114e-001 -7.45047e-002
+ 12Z+: -1.29466e-001 -1.32230e-001
+ 13X-: -4.18692e-002 -2.69841e-002
+ 13Y-: -2.20607e-002 5.52757e-003
+ 13Z+: -2.78354e-003 -2.58512e-002
+ 14X-: 2.81964e-003 -1.16547e-002
+ 14Y-: -1.69386e-002 7.56441e-003
+ 14Z+: -4.47088e-002 1.62166e-002
+ 15X-: 1.34640e-002 -8.44759e-003
+ 15Y-: -1.94624e-002 1.71758e-002
+ 15Z+: -4.86313e-003 2.88246e-004
+ 16X-: 4.26640e-002 8.79228e-003
+ 16Y-: 4.80505e-002 5.29679e-002
+ 16Z+: 1.27040e-001 1.24874e-002
+ 17X-: -8.10538e-003 -8.30561e-003
+ 17Y-: 1.34544e-002 9.35265e-003
+ 17Z+: 1.46109e-002 -3.56062e-003
+ 18X-: 3.84284e-003 -1.31171e-002
+ 18Y-: 1.88100e-003 7.10407e-003
+ 18Z+: -3.74849e-002 4.55493e-002
+ 19X-: 2.48711e-002 4.50694e-004
+ 19Y-: -2.71848e-002 4.78831e-003
+ 19Z+: 3.79650e-003 8.15474e-003
+ 20X-: -1.72280e-003 -1.00320e-002
+ 20Y-: -1.28490e-002 1.10258e-002
+ 20Z+: 5.02243e-002 -4.71354e-002
+ 21X-: -7.29017e-002 -1.35859e-001
+ 21Y-: 6.97213e-002 6.46475e-002
+ 21Z+: 1.06365e-001 2.83730e-002
+ 22X-: -6.40308e-002 -1.11085e-001
+ 22Y-: 4.14298e-002 3.36296e-002
+ 22Z+: 2.56521e-002 1.33000e-002
+ 23X-: -8.52167e-002 -1.42715e-001
+ 23Z+: 3.65832e-003 -9.76287e-003
+ 23Y+: -5.04224e-002 -2.22359e-002
+
+Mode 5
+freq = 53.99524Hz
+damp = 0.24170%
+modal A = -6.02120e+005-5.53574e+004i
+modal B = -1.92744e+007+2.04231e+008i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 2.04797e-002 -1.34329e-002
+ 1Y-: 8.93985e-002 3.54369e-002
+ 1Z+: 5.47779e-001 2.77556e-017
+ 2X-: 8.04989e-002 8.92988e-003
+ 2Y-: 1.23888e-001 4.47265e-002
+ 2Z+: 2.76589e-001 -2.74537e-003
+ 3Y-: -8.80396e-003 2.11963e-002
+ 3X+: -3.03476e-002 1.07320e-003
+ 3Z+: -1.79362e-001 -7.72148e-003
+ 4X-: -3.98937e-003 -2.65338e-002
+ 4Y-: -4.24391e-002 5.95176e-002
+ 4Z+: 1.90265e-001 -2.05203e-004
+ 5X-: -3.07310e-002 2.84849e-004
+ 5Y-: -2.15985e-001 1.03322e-001
+ 5Z+: 2.64936e-001 -3.99819e-002
+ 6X-: -5.67429e-002 -5.15296e-002
+ 6Y-: -1.57237e-001 -7.16569e-003
+ 6Z+: 7.88352e-002 -4.70567e-002
+ 7X-: -5.30646e-002 -4.24721e-002
+ 7Y-: -5.23393e-002 6.65755e-002
+ 7Z+: 4.26957e-002 4.41942e-002
+ 8X-: -5.68539e-002 -2.52856e-002
+ 8Y-: -7.57448e-002 4.98787e-002
+ 8Z+: 1.71653e-001 3.18524e-002
+ 9X-: -1.81063e-002 2.14848e-002
+ 9Y-: -9.24072e-002 -1.71215e-002
+ 9Z+: 2.04804e-001 -5.93099e-003
+ 10X-: -3.22900e-002 -1.01768e-002
+ 10Y-: -8.52719e-002 -9.25570e-003
+ 10Z+: 2.01874e-002 2.67909e-004
+ 11X-: -2.68470e-002 -2.06802e-002
+ 11Y-: -4.85455e-003 4.47463e-002
+ 11Z+: -4.48055e-003 -5.86717e-003
+ 12X-: -4.65608e-002 2.18137e-002
+ 12Y-: -9.79897e-002 -2.74631e-004
+ 12Z+: 9.94627e-002 -4.24783e-002
+ 13X-: -3.27943e-002 7.62233e-005
+ 13Y-: -3.98493e-002 -2.94026e-003
+ 13Z+: 3.19110e-002 -2.39178e-002
+ 14X-: -1.52795e-002 -1.04948e-003
+ 14Y-: -3.29619e-002 -6.50682e-004
+ 14Z+: -2.51551e-002 -1.16355e-002
+ 15X-: -1.96760e-002 1.29422e-003
+ 15Y-: -3.53204e-002 8.80410e-003
+ 15Z+: 1.86992e-003 2.36834e-004
+ 16X-: 5.54951e-002 5.42763e-002
+ 16Y-: 4.85407e-002 7.12644e-002
+ 16Z+: 1.51342e-001 5.89061e-002
+ 17X-: -5.80957e-003 1.12796e-002
+ 17Y-: -1.19505e-002 1.18421e-002
+ 17Z+: 5.22411e-002 -1.02807e-002
+ 18X-: -1.44878e-002 -2.41785e-003
+ 18Y-: -2.42828e-002 1.53646e-003
+ 18Z+: -1.14173e-002 4.33203e-003
+ 19X-: -2.75346e-003 5.57986e-003
+ 19Y-: -1.84250e-002 1.49897e-002
+ 19Z+: -2.60771e-002 6.58908e-003
+ 20X-: -9.42255e-003 1.14575e-002
+ 20Y-: -1.57054e-002 2.10317e-002
+ 20Z+: 6.41005e-002 -2.34521e-002
+ 21X-: -1.42418e-002 -6.30318e-002
+ 21Y-: -6.74634e-002 6.33271e-002
+ 21Z+: 2.26786e-001 -5.37533e-002
+ 22X-: -1.22583e-001 -7.35745e-003
+ 22Y-: -3.58157e-002 2.30221e-002
+ 22Z+: 1.12655e-001 -2.80870e-002
+ 23X-: -3.19992e-002 -6.51145e-002
+ 23Z+: 1.86196e-001 -1.34683e-002
+ 23Y+: -4.58487e-002 8.95616e-003
+
+Mode 6
+freq = 56.14871Hz
+damp = 2.83603%
+modal A = -8.13722e+003-4.17194e+004i
+modal B = -1.47938e+007+2.45218e+006i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: -2.23217e-002 -2.24908e-002
+ 1Y-: -1.63353e-001 3.11716e-002
+ 1Z+: 2.75707e-001 -4.06196e-003
+ 2X-: -2.62772e-002 1.36639e-002
+ 2Y-: -1.62875e-001 3.44557e-002
+ 2Z+: 2.33889e-001 4.40946e-003
+ 3Y-: -1.60361e-001 1.46455e-002
+ 3X+: 7.56256e-003 -9.89230e-003
+ 3Z+: 2.31547e-001 3.21404e-002
+ 4X-: -1.24095e-002 -1.94291e-002
+ 4Y-: -1.78799e-001 2.53382e-002
+ 4Z+: 2.55423e-001 2.84919e-002
+ 5X-: 4.73388e-002 -1.28660e-002
+ 5Y-: -1.84614e-001 -5.92289e-002
+ 5Z+: 3.13466e-001 0.00000e+000
+ 6X-: -2.22430e-002 -1.38898e-002
+ 6Y-: -1.42423e-001 1.31834e-002
+ 6Z+: 1.39780e-001 -1.75543e-002
+ 7X-: -3.81741e-002 -1.15445e-002
+ 7Y-: -8.72665e-003 1.17039e-002
+ 7Z+: 7.82984e-002 2.25712e-002
+ 8X-: 1.65383e-002 -2.22563e-002
+ 8Y-: -8.09816e-003 1.35995e-002
+ 8Z+: 2.36612e-001 3.72090e-002
+ 9X-: 3.54981e-002 -2.50223e-003
+ 9Y-: -1.12182e-001 2.48552e-002
+ 9Z+: 2.22972e-001 1.77196e-002
+ 10X-: -5.52031e-002 -8.14062e-003
+ 10Y-: -1.13900e-001 9.55516e-004
+ 10Z+: 6.48413e-002 1.52394e-002
+ 11X-: -6.84433e-002 -1.54853e-002
+ 11Y-: 3.28543e-002 2.04550e-002
+ 11Z+: 1.86434e-002 -1.07188e-002
+ 12X-: -2.18097e-002 -2.62513e-002
+ 12Y-: -2.87698e-002 -2.29940e-002
+ 12Z+: 2.07008e-001 3.40250e-003
+ 13X-: -3.38262e-002 -1.36788e-002
+ 13Y-: -2.46909e-002 -9.46523e-003
+ 13Z+: 4.81575e-002 -1.08069e-002
+ 14X-: -2.88523e-002 -2.56869e-003
+ 14Y-: -2.61372e-002 -4.98577e-003
+ 14Z+: 2.08749e-002 -5.65494e-003
+ 15X-: -3.13905e-002 -4.09507e-003
+ 15Y-: -2.09029e-002 1.23168e-003
+ 15Z+: 1.02131e-002 4.24828e-003
+ 16X-: 2.05922e-002 4.45681e-002
+ 16Y-: 1.08079e-002 6.46630e-002
+ 16Z+: 8.96188e-002 7.25567e-002
+ 17X-: -3.71171e-003 3.06109e-003
+ 17Y-: -1.98477e-002 5.42124e-003
+ 17Z+: 5.22931e-002 4.14686e-003
+ 18X-: -2.30328e-002 -5.01749e-003
+ 18Y-: -2.67478e-002 -1.58019e-004
+ 18Z+: 2.67701e-002 1.37761e-002
+ 19X-: -2.39130e-002 1.72765e-003
+ 19Y-: -3.27778e-003 9.44237e-003
+ 19Z+: -2.15535e-002 2.87797e-003
+ 20X-: -7.52190e-003 1.23387e-003
+ 20Y-: -3.28211e-003 1.11381e-002
+ 20Z+: 5.02438e-002 -4.73666e-003
+ 21X-: 2.50859e-002 -3.14849e-002
+ 21Y-: -1.44095e-002 5.42084e-002
+ 21Z+: 2.95947e-001 8.46057e-002
+ 22X-: -8.31761e-003 -1.47119e-002
+ 22Y-: -6.90347e-003 3.16323e-002
+ 22Z+: 1.81434e-001 5.70176e-002
+ 23X-: 2.16238e-002 -3.86014e-002
+ 23Z+: 2.54047e-001 8.33776e-002
+ 23Y+: -1.86398e-002 -2.38212e-002
+
+Mode 7
+freq = 69.68561Hz
+damp = 4.60472%
+modal A = 9.12802e+003-3.78264e+004i
+modal B = -1.63606e+007-4.75508e+006i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 3.49042e-001 0.00000e+000
+ 1Y-: 6.72195e-002 2.74443e-002
+ 1Z+: 1.86218e-002 -5.19569e-003
+ 2X-: 3.19009e-001 -3.95993e-002
+ 2Y-: 5.27871e-002 2.90767e-002
+ 2Z+: -5.08006e-003 -5.61494e-003
+ 3Y-: 1.30972e-001 5.26789e-002
+ 3X+: -3.27411e-001 4.68165e-002
+ 3Z+: 6.05823e-002 -1.21134e-002
+ 4X-: 3.27800e-001 -3.37937e-003
+ 4Y-: 8.14429e-002 5.89840e-002
+ 4Z+: 7.83298e-002 5.26937e-004
+ 5X-: 2.55289e-002 6.00522e-003
+ 5Y-: -1.59558e-004 4.06808e-002
+ 5Z+: -1.48819e-001 -1.13372e-002
+ 6X-: 1.57928e-001 -1.60751e-002
+ 6Y-: 1.19190e-001 -2.37349e-002
+ 6Z+: -8.06133e-002 -2.20152e-002
+ 7X-: 1.49041e-001 -1.58152e-002
+ 7Y-: -1.44523e-001 1.27320e-002
+ 7Z+: 1.87294e-001 2.21839e-002
+ 8X-: 6.52434e-002 -1.85023e-003
+ 8Y-: -8.76775e-002 1.02981e-002
+ 8Z+: 2.00438e-001 1.85099e-002
+ 9X-: 1.28713e-001 1.46507e-002
+ 9Y-: 1.02129e-001 -1.83169e-002
+ 9Z+: -1.06258e-001 -1.16411e-002
+ 10X-: 2.10921e-001 1.07813e-003
+ 10Y-: 9.64026e-002 -2.32810e-003
+ 10Z+: -1.19838e-002 -1.33333e-003
+ 11X-: 2.14695e-001 -1.59566e-003
+ 11Y-: -1.08768e-001 2.67876e-002
+ 11Z+: 9.14694e-002 8.79700e-003
+ 12X-: 1.05023e-001 1.40876e-002
+ 12Y-: -5.17509e-002 1.53104e-002
+ 12Z+: 7.03962e-002 2.82254e-002
+ 13X-: 2.83208e-002 -1.71314e-002
+ 13Y-: 9.98870e-002 -2.29528e-003
+ 13Z+: -4.48858e-002 4.04403e-003
+ 14X-: 7.76998e-002 -5.82289e-003
+ 14Y-: 1.01022e-001 -5.97748e-005
+ 14Z+: 5.59344e-002 -4.02364e-003
+ 15X-: 6.98240e-002 -3.75708e-003
+ 15Y-: 5.74518e-002 -1.28987e-002
+ 15Z+: 3.88446e-002 -5.95002e-003
+ 16X-: -3.12391e-002 -1.86023e-002
+ 16Y-: 1.32651e-003 -1.40105e-002
+ 16Z+: -1.29901e-001 5.88813e-003
+ 17X-: 4.97985e-003 -2.00275e-002
+ 17Y-: 7.41657e-002 8.92606e-003
+ 17Z+: -7.31670e-002 6.30394e-003
+ 18X-: 6.36562e-002 2.42169e-003
+ 18Y-: 9.65414e-002 9.19014e-003
+ 18Z+: 5.65499e-002 -4.93422e-003
+ 19X-: 6.05389e-002 7.83715e-003
+ 19Y-: 2.44416e-002 -1.99510e-002
+ 19Z+: 7.35773e-002 -5.55097e-003
+ 20X-: 1.19417e-002 -1.62195e-002
+ 20Y-: 1.15389e-002 -1.66778e-002
+ 20Z+: -4.80762e-002 1.04955e-002
+ 21X-: 4.66618e-002 -1.54758e-002
+ 21Y-: -3.32029e-002 8.51119e-004
+ 21Z+: -1.91004e-002 -6.10273e-003
+ 22X-: 3.04779e-002 -1.66685e-002
+ 22Y-: -9.20565e-003 -5.98560e-005
+ 22Z+: 6.74300e-002 1.97858e-003
+ 23X-: 5.15793e-002 -1.51840e-002
+ 23Z+: 1.01942e-001 9.63720e-003
+ 23Y+: 6.87391e-003 -7.71313e-004
+
+Mode 8
+freq = 71.58533Hz
+damp = 0.64145%
+modal A = 1.83523e+005-5.45837e+005i
+modal B = -2.44974e+008-8.41188e+007i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 2.54106e-001 6.93889e-018
+ 1Y-: 5.78914e-002 9.55918e-002
+ 1Z+: 3.95429e-002 -2.81699e-002
+ 2X-: 1.83133e-001 -1.78256e-002
+ 2Y-: 4.26620e-002 1.10443e-001
+ 2Z+: -2.39331e-003 -8.82299e-002
+ 3Y-: 1.47879e-001 1.47626e-001
+ 3X+: -1.68268e-001 2.90811e-003
+ 3Z+: 4.50393e-002 -2.70454e-002
+ 4X-: 2.33894e-001 -2.04415e-002
+ 4Y-: 1.29407e-001 1.30677e-001
+ 4Z+: 8.93868e-002 -3.90882e-003
+ 5X-: 9.33085e-002 -3.11533e-003
+ 5Y-: -1.67558e-001 -1.16756e-001
+ 5Z+: -2.89490e-002 -8.40203e-002
+ 6X-: 1.86621e-001 -2.12998e-002
+ 6Y-: 3.00339e-002 1.07630e-002
+ 6Z+: 1.77230e-002 -3.06254e-002
+ 7X-: 1.72044e-001 -2.64201e-002
+ 7Y-: -1.54440e-001 -9.58419e-003
+ 7Z+: 8.01945e-002 -2.10080e-002
+ 8X-: 1.54694e-001 2.37482e-002
+ 8Y-: -1.03718e-001 4.94800e-002
+ 8Z+: 1.67888e-001 -5.86624e-002
+ 9X-: 1.40016e-001 -1.26706e-002
+ 9Y-: 3.27501e-003 6.39236e-003
+ 9Z+: -2.35127e-002 -1.09321e-001
+ 10X-: 1.75309e-001 -2.82343e-002
+ 10Y-: 1.08100e-002 2.57585e-002
+ 10Z+: -2.51793e-002 1.13681e-002
+ 11X-: 2.04662e-001 -4.03398e-002
+ 11Y-: -1.29117e-001 3.82380e-002
+ 11Z+: 9.87303e-002 -5.72286e-002
+ 12X-: 1.54977e-001 -5.34601e-002
+ 12Y-: -7.72552e-002 1.05211e-001
+ 12Z+: 1.35542e-001 -3.49892e-002
+ 13X-: 9.43376e-002 -4.22021e-002
+ 13Y-: 7.74119e-002 2.49376e-002
+ 13Z+: -1.23082e-002 -2.52471e-002
+ 14X-: 7.65199e-002 1.62040e-002
+ 14Y-: 6.67836e-002 3.45945e-002
+ 14Z+: 3.68570e-002 2.01591e-002
+ 15X-: 6.03285e-002 2.17135e-002
+ 15Y-: 7.04655e-002 -1.46762e-002
+ 15Z+: 4.58970e-002 -4.79051e-003
+ 16X-: 9.27179e-003 -9.94695e-002
+ 16Y-: -1.59890e-002 -5.48971e-002
+ 16Z+: -1.38731e-001 -6.80828e-002
+ 17X-: 6.27109e-002 -7.11393e-002
+ 17Y-: 2.93292e-002 4.14498e-002
+ 17Z+: -7.48289e-002 -1.61067e-002
+ 18X-: 5.34387e-002 3.13596e-002
+ 18Y-: 5.03017e-002 6.25287e-002
+ 18Z+: 1.71172e-002 2.39424e-002
+ 19X-: 2.29605e-002 4.42650e-002
+ 19Y-: 7.55904e-002 -7.11189e-002
+ 19Z+: 6.81520e-002 1.13929e-002
+ 20X-: 6.20574e-002 -6.62008e-002
+ 20Y-: 4.75443e-002 -6.73388e-002
+ 20Z+: -6.39034e-003 -1.40658e-002
+ 21X-: 1.51199e-001 -1.36670e-002
+ 21Y-: -7.90908e-002 -5.96052e-003
+ 21Z+: 4.93456e-002 -7.19582e-002
+ 22X-: 1.37920e-001 -4.32860e-002
+ 22Y-: -4.27728e-002 1.75229e-002
+ 22Z+: 7.24573e-002 -3.05564e-002
+ 23X-: 1.67732e-001 -2.40449e-002
+ 23Z+: 1.25286e-001 -8.53890e-002
+ 23Y+: 4.86745e-002 -3.23812e-002
+
+Mode 9
+freq = 72.35341Hz
+damp = 1.58544%
+modal A = -1.85481e+005-8.15852e+004i
+modal B = -3.84216e+007+8.37228e+007i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 1.36051e-001 -4.89415e-003
+ 1Y-: -4.86172e-003 -2.89055e-002
+ 1Z+: 2.28917e-002 -9.95448e-003
+ 2X-: 1.25418e-001 1.51945e-004
+ 2Y-: -1.94714e-002 -3.92149e-002
+ 2Z+: 1.16559e-002 -4.29402e-002
+ 3Y-: 1.70504e-002 -2.55843e-002
+ 3X+: -1.15187e-001 -1.74116e-002
+ 3Z+: 4.05257e-002 -5.50849e-002
+ 4X-: 1.56306e-001 9.53597e-003
+ 4Y-: 5.44631e-002 -9.85494e-002
+ 4Z+: 7.06520e-002 -6.57143e-002
+ 5X-: -2.09558e-002 1.01625e-002
+ 5Y-: -1.11286e-002 -2.16906e-001
+ 5Z+: -4.26074e-002 2.07531e-002
+ 6X-: 1.59724e-001 6.14303e-002
+ 6Y-: 1.30562e-001 -7.49435e-003
+ 6Z+: -1.07016e-002 6.67568e-002
+ 7X-: 1.35917e-001 5.12977e-002
+ 7Y-: -1.58600e-001 -8.86530e-002
+ 7Z+: 5.86814e-002 -1.17092e-001
+ 8X-: 1.93633e-002 1.10504e-001
+ 8Y-: -1.41017e-001 -3.29504e-002
+ 8Z+: 1.33151e-001 -7.30661e-002
+ 9X-: 7.54127e-002 -1.45050e-002
+ 9Y-: 8.84524e-002 -3.29862e-002
+ 9Z+: 7.65206e-002 -3.31688e-002
+ 10X-: 1.35093e-001 2.94046e-002
+ 10Y-: 7.43957e-002 -1.86002e-002
+ 10Z+: -4.33450e-002 -1.66312e-002
+ 11X-: 1.60081e-001 6.48140e-002
+ 11Y-: -1.64489e-001 -5.38955e-002
+ 11Z+: 8.64030e-002 7.62012e-005
+ 12X-: 8.51100e-002 2.50195e-002
+ 12Y-: -1.24567e-001 4.73137e-002
+ 12Z+: -1.54578e-002 8.00685e-002
+ 13X-: 1.86292e-001 1.48671e-002
+ 13Y-: -3.06131e-004 2.60090e-002
+ 13Z+: -3.51976e-003 2.91627e-002
+ 14X-: -1.18393e-002 2.68534e-002
+ 14Y-: -3.42452e-002 2.31617e-002
+ 14Z+: 5.07813e-003 2.68979e-002
+ 15X-: -2.38097e-002 1.77339e-002
+ 15Y-: 1.52190e-001 -1.74922e-002
+ 15Z+: 3.58511e-002 4.47742e-004
+ 16X-: 1.46203e-001 -1.06160e-001
+ 16Y-: 7.74000e-002 -1.45161e-001
+ 16Z+: -1.15768e-001 -1.63022e-001
+ 17X-: 1.98981e-001 -7.77150e-003
+ 17Y-: -1.02595e-001 -2.90007e-002
+ 17Z+: -7.03751e-002 -1.07213e-002
+ 18X-: -6.31906e-002 1.36258e-002
+ 18Y-: -1.09602e-001 -3.02975e-003
+ 18Z+: -1.05120e-002 -2.87067e-002
+ 19X-: -1.09079e-001 -2.77680e-002
+ 19Y-: 2.59313e-001 -2.77556e-017
+ 19Z+: 7.82537e-002 -9.70229e-003
+ 20X-: 1.96662e-001 -4.49444e-003
+ 20Y-: 2.22366e-001 -2.08580e-002
+ 20Z+: -5.31544e-002 2.35321e-002
+ 21X-: 5.60174e-002 1.43726e-001
+ 21Y-: -3.11671e-002 -1.29216e-001
+ 21Z+: 2.71581e-002 -1.50583e-002
+ 22X-: 7.32382e-002 5.18719e-002
+ 22Y-: -2.51819e-002 -4.76929e-002
+ 22Z+: 4.60840e-002 -3.53280e-002
+ 23X-: 7.18342e-002 1.50518e-001
+ 23Z+: 1.03031e-001 -5.92741e-002
+ 23Y+: 4.71315e-002 6.83467e-003
+
+Mode 10
+freq = 84.92538Hz
+damp = 3.56361%
+modal A = -6.44647e+003-3.91843e+004i
+modal B = -2.10181e+007+2.69256e+006i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 3.36633e-001 1.01212e-003
+ 1Y-: 2.61798e-001 -2.97763e-002
+ 1Z+: -1.38203e-002 8.87316e-003
+ 2X-: 3.67742e-001 0.00000e+000
+ 2Y-: 2.45246e-001 -4.17421e-002
+ 2Z+: -4.12293e-002 9.30803e-003
+ 3Y-: 2.84468e-001 -2.62459e-002
+ 3X+: -3.35385e-001 6.49840e-003
+ 3Z+: -4.40848e-003 1.07473e-003
+ 4X-: 3.34843e-001 2.47667e-002
+ 4Y-: 2.56218e-001 -1.55672e-002
+ 4Z+: 1.80977e-002 -7.49140e-003
+ 5X-: -1.74708e-002 4.38023e-002
+ 5Y-: -2.06499e-001 -8.62042e-002
+ 5Z+: -8.82122e-002 -3.14007e-002
+ 6X-: 4.97008e-002 6.60595e-002
+ 6Y-: 3.53572e-002 -2.71147e-002
+ 6Z+: -1.62267e-002 -3.99986e-003
+ 7X-: 2.58045e-002 5.73363e-002
+ 7Y-: -8.08744e-002 -4.29921e-002
+ 7Z+: 4.93456e-002 -2.99090e-003
+ 8X-: 5.39461e-002 8.19648e-002
+ 8Y-: -3.22240e-002 -3.65877e-002
+ 8Z+: 7.43713e-002 3.06607e-002
+ 9X-: 1.27900e-002 4.76350e-002
+ 9Y-: 9.96729e-003 -2.47347e-002
+ 9Z+: -5.39684e-002 -1.78201e-002
+ 10X-: 5.46419e-002 7.18302e-002
+ 10Y-: 1.71585e-002 -8.72984e-003
+ 10Z+: -9.88239e-003 -3.01221e-002
+ 11X-: 7.45042e-002 1.06122e-001
+ 11Y-: -7.02643e-002 -2.68660e-002
+ 11Z+: 2.75211e-002 5.34362e-002
+ 12X-: 2.29130e-002 8.93237e-002
+ 12Y-: -7.81618e-003 -2.82637e-002
+ 12Z+: 5.19432e-002 8.81927e-002
+ 13X-: -1.23657e-002 1.86807e-002
+ 13Y-: -1.65194e-002 3.80460e-003
+ 13Z+: 2.61127e-002 2.35554e-002
+ 14X-: -1.90129e-002 1.56308e-002
+ 14Y-: -1.55611e-002 3.99374e-003
+ 14Z+: 3.68544e-002 -1.13741e-003
+ 15X-: -2.73892e-002 5.14115e-003
+ 15Y-: -2.96516e-002 -1.38455e-002
+ 15Z+: -6.07740e-003 9.63281e-003
+ 16X-: -8.50488e-002 -1.97717e-002
+ 16Y-: -9.32924e-002 -4.71051e-002
+ 16Z+: -9.14319e-002 -2.38909e-002
+ 17X-: -2.74319e-002 8.21299e-004
+ 17Y-: -3.70313e-002 -7.22124e-003
+ 17Z+: 2.57187e-002 5.35510e-003
+ 18X-: -1.06301e-002 1.17978e-002
+ 18Y-: -2.30481e-002 -8.51425e-004
+ 18Z+: 1.84786e-002 -2.47425e-002
+ 19X-: -3.02233e-002 -1.55486e-003
+ 19Y-: -3.43476e-002 -8.06727e-003
+ 19Z+: -3.41121e-002 -4.71628e-003
+ 20X-: -4.14086e-002 -5.84715e-003
+ 20Y-: -4.24504e-002 -1.87934e-002
+ 20Z+: -1.93120e-002 4.41500e-002
+ 21X-: 2.58203e-002 8.56429e-002
+ 21Y-: -5.31291e-002 -6.04372e-002
+ 21Z+: -3.33293e-002 -4.01927e-003
+ 22X-: 5.99064e-003 4.85390e-002
+ 22Y-: -2.47232e-002 -2.94661e-002
+ 22Z+: 2.02294e-002 -7.30045e-003
+ 23X-: 3.46052e-002 9.17653e-002
+ 23Z+: 3.06757e-002 2.15102e-002
+ 23Y+: 2.36604e-002 1.62460e-002
+
+Mode 11
+freq = 90.56538Hz
+damp = 0.26865%
+modal A = 2.02548e+005-4.85436e+005i
+modal B = -2.75921e+008-1.15999e+008i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 2.67708e-002 2.74525e-001
+ 1Y-: -2.91694e-001 -1.07158e-001
+ 1Z+: 9.69310e-005 -8.00019e-003
+ 2X-: -5.76651e-002 2.20984e-001
+ 2Y-: -2.91098e-001 -1.12103e-001
+ 2Z+: -4.69992e-002 -8.76333e-002
+ 3Y-: -2.36027e-001 -3.10584e-002
+ 3X+: 3.99562e-002 -2.35161e-001
+ 3Z+: -1.75207e-002 -1.80121e-003
+ 4X-: 4.92887e-002 2.62766e-001
+ 4Y-: -3.34686e-001 -1.22223e-001
+ 4Z+: 1.15472e-002 6.89684e-002
+ 5X-: 9.31525e-002 4.30274e-002
+ 5Y-: 4.28742e-001 0.00000e+000
+ 5Z+: 1.20315e-001 -6.88546e-003
+ 6X-: 2.14438e-002 6.42612e-002
+ 6Y-: -6.00127e-002 3.47543e-002
+ 6Z+: 4.48069e-002 -4.50366e-002
+ 7X-: 4.12093e-002 6.60117e-002
+ 7Y-: 6.34667e-002 -5.20025e-002
+ 7Z+: -9.54154e-002 -1.99214e-002
+ 8X-: -4.58596e-003 2.39357e-002
+ 8Y-: -2.20034e-002 -4.37492e-002
+ 8Z+: -1.12515e-001 4.80694e-002
+ 9X-: 9.94105e-003 4.13831e-002
+ 9Y-: -5.98241e-002 2.66145e-002
+ 9Z+: 4.62800e-002 -2.15276e-002
+ 10X-: -4.73879e-003 2.75708e-002
+ 10Y-: -4.51676e-002 3.44461e-002
+ 10Z+: -8.72004e-003 -2.96813e-002
+ 11X-: -2.00980e-002 1.74389e-002
+ 11Y-: -1.20815e-002 -5.91287e-002
+ 11Z+: 5.07893e-002 -1.09888e-002
+ 12X-: 7.97075e-002 -6.47558e-005
+ 12Y-: -3.52120e-002 -4.11831e-002
+ 12Z+: 8.07086e-002 3.49300e-003
+ 13X-: 1.55242e-002 -1.33450e-002
+ 13Y-: 2.83984e-002 -3.37738e-002
+ 13Z+: 1.61918e-002 5.68178e-004
+ 14X-: 7.96841e-003 -2.00488e-002
+ 14Y-: 1.80342e-002 -3.17335e-002
+ 14Z+: -1.14509e-002 -3.63285e-003
+ 15X-: 1.82173e-002 -1.52054e-002
+ 15Y-: 6.89124e-003 -2.29847e-002
+ 15Z+: -9.04429e-003 -2.00318e-002
+ 16X-: 1.13032e-002 -1.59312e-002
+ 16Y-: -2.12802e-002 -2.18411e-002
+ 16Z+: -6.22788e-003 -6.12421e-003
+ 17X-: 1.19917e-002 -1.02466e-002
+ 17Y-: 3.32613e-002 -3.01284e-002
+ 17Z+: -1.04610e-002 1.93512e-002
+ 18X-: 1.54219e-002 -1.58321e-002
+ 18Y-: 1.94304e-002 -3.17964e-002
+ 18Z+: -2.34641e-002 6.06564e-003
+ 19X-: 2.09708e-002 -1.47951e-002
+ 19Y-: -3.84825e-003 -2.45949e-002
+ 19Z+: -1.20723e-002 -3.09086e-002
+ 20X-: 2.28717e-002 -1.01798e-002
+ 20Y-: 9.31470e-003 -1.78015e-002
+ 20Z+: 1.96218e-002 -3.22857e-002
+ 21X-: 6.52121e-002 2.63049e-002
+ 21Y-: -3.28285e-002 6.46229e-003
+ 21Z+: 4.58092e-002 7.48103e-003
+ 22X-: 1.00322e-001 2.85765e-002
+ 22Y-: -3.56968e-002 6.90330e-003
+ 22Z+: -5.61545e-002 6.03258e-003
+ 23X-: 7.74661e-002 2.53268e-002
+ 23Z+: -3.54944e-002 -6.46860e-003
+ 23Y+: 4.80571e-002 -1.21643e-002
+
+Mode 12
+freq = 91.00542Hz
+damp = 2.86851%
+modal A = -1.54209e+002-3.09920e+004i
+modal B = -1.77166e+007-4.20197e+005i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: -3.71679e-002 4.63472e-002
+ 1Y-: 4.56372e-001 -4.08327e-003
+ 1Z+: 3.73915e-002 -3.01330e-002
+ 2X-: 4.36097e-002 9.43540e-002
+ 2Y-: 4.58132e-001 -6.93889e-018
+ 2Z+: 1.30567e-001 -9.70513e-002
+ 3Y-: 4.07785e-001 -3.62856e-002
+ 3X+: 2.37126e-002 -9.22382e-002
+ 3Z+: 1.88102e-002 -4.88296e-004
+ 4X-: -5.32016e-002 5.30662e-002
+ 4Y-: 4.32166e-001 4.00806e-003
+ 4Z+: -6.12119e-002 5.64503e-002
+ 5X-: -2.97213e-002 -2.67904e-003
+ 5Y-: -1.30219e-001 1.55389e-001
+ 5Z+: 3.14593e-002 -5.15102e-002
+ 6X-: -5.36298e-002 1.75840e-002
+ 6Y-: -5.22730e-002 6.99334e-002
+ 6Z+: 5.60704e-002 -3.81261e-002
+ 7X-: -6.59233e-002 3.24221e-002
+ 7Y-: 4.98861e-002 -1.30300e-002
+ 7Z+: 5.54869e-003 4.27486e-002
+ 8X-: -2.48500e-002 -2.69021e-002
+ 8Y-: 3.86003e-002 -1.37636e-002
+ 8Z+: -4.72029e-002 3.71726e-002
+ 9X-: -4.79246e-002 1.75448e-002
+ 9Y-: -2.23094e-002 5.74662e-002
+ 9Z+: 5.01077e-002 -3.55142e-002
+ 10X-: -5.50025e-002 6.22260e-003
+ 10Y-: -3.51629e-002 4.41439e-002
+ 10Z+: 3.33247e-002 9.26731e-003
+ 11X-: -4.84759e-002 -1.39084e-002
+ 11Y-: 5.39589e-002 -5.56735e-003
+ 11Z+: -1.31155e-002 1.07976e-002
+ 12X-: -4.63102e-002 -4.43476e-003
+ 12Y-: -3.72730e-003 -1.05107e-002
+ 12Z+: -7.51602e-002 -1.80961e-002
+ 13X-: 1.86094e-002 -1.87627e-002
+ 13Y-: -1.19504e-002 -1.60662e-002
+ 13Z+: -7.25740e-003 -4.47565e-003
+ 14X-: 2.25561e-002 -2.62249e-002
+ 14Y-: -7.81923e-003 -1.50539e-002
+ 14Z+: -3.59901e-002 1.69283e-002
+ 15X-: 1.69466e-002 -1.93596e-002
+ 15Y-: -1.66055e-003 -4.66286e-003
+ 15Z+: 2.02723e-002 -7.42334e-003
+ 16X-: 7.94794e-002 3.41391e-004
+ 16Y-: 7.47599e-002 1.55768e-002
+ 16Z+: 1.13538e-001 2.49585e-002
+ 17X-: 2.33545e-002 -1.08534e-002
+ 17Y-: 9.15834e-003 -1.23520e-002
+ 17Z+: -4.60076e-003 1.80799e-002
+ 18X-: 1.17619e-002 -2.24206e-002
+ 18Y-: 2.65104e-003 -1.88788e-002
+ 18Z+: -2.92551e-002 3.59404e-002
+ 19X-: 2.11272e-002 -1.51246e-002
+ 19Y-: 2.00077e-002 -7.37891e-003
+ 19Z+: 2.94142e-002 -1.07761e-002
+ 20X-: 2.37821e-002 -7.92793e-003
+ 20Y-: 1.41737e-002 2.18666e-003
+ 20Z+: 5.83851e-002 -2.72385e-002
+ 21X-: -2.62161e-002 -3.38875e-002
+ 21Y-: 1.98168e-002 3.91595e-002
+ 21Z+: 3.49111e-002 -1.36610e-002
+ 22X-: -3.10830e-002 -1.19053e-002
+ 22Y-: 9.28009e-003 2.14164e-002
+ 22Z+: 2.39367e-002 1.16607e-002
+ 23X-: -3.34802e-002 -3.73525e-002
+ 23Z+: -4.61993e-003 -1.12761e-003
+ 23Y+: -1.70684e-002 -1.28953e-002
+
+Mode 13
+freq = 95.76079Hz
+damp = 3.30737%
+modal A = 2.10759e+004-1.47578e+004i
+modal B = -8.45524e+006-1.29677e+007i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 4.34246e-001 0.00000e+000
+ 1Y-: -3.09884e-002 2.92583e-002
+ 1Z+: 6.84765e-003 -1.65203e-002
+ 2X-: 3.91045e-001 -5.86271e-002
+ 2Y-: -5.59852e-002 3.21685e-002
+ 2Z+: -8.70522e-003 9.18637e-002
+ 3Y-: 6.00857e-002 7.55405e-002
+ 3X+: -3.77571e-001 4.61188e-002
+ 3Z+: -1.62061e-002 4.04115e-002
+ 4X-: 4.32975e-001 6.48773e-003
+ 4Y-: 2.74295e-002 1.10882e-001
+ 4Z+: 8.23424e-004 -4.05886e-002
+ 5X-: 2.11610e-002 2.56613e-002
+ 5Y-: -3.62145e-002 6.58836e-002
+ 5Z+: 1.03284e-001 -1.19474e-001
+ 6X-: -1.91560e-002 7.56709e-002
+ 6Y-: -1.04518e-001 1.02256e-001
+ 6Z+: 3.19482e-002 -6.99689e-002
+ 7X-: -1.03581e-002 8.27073e-002
+ 7Y-: 2.81680e-002 -3.50976e-002
+ 7Z+: -9.84763e-002 1.03930e-001
+ 8X-: 2.21990e-003 8.10310e-003
+ 8Y-: -2.26999e-002 -2.76729e-002
+ 8Z+: -6.62504e-002 1.04660e-001
+ 9X-: -3.27732e-002 7.68258e-002
+ 9Y-: -7.73259e-002 1.08871e-001
+ 9Z+: 9.12983e-002 -6.50589e-002
+ 10X-: -3.43740e-002 8.88737e-002
+ 10Y-: -6.51529e-002 1.05867e-001
+ 10Z+: -3.00013e-002 -1.79417e-002
+ 11X-: -5.52268e-003 7.93508e-002
+ 11Y-: 1.62745e-002 -2.73164e-002
+ 11Z+: -3.50758e-003 3.81859e-002
+ 12X-: 2.99644e-003 6.03189e-002
+ 12Y-: -5.99114e-002 -6.39997e-002
+ 12Z+: 2.39116e-002 -2.04029e-002
+ 13X-: 1.22572e-002 -1.21522e-002
+ 13Y-: 6.87633e-003 -6.77783e-002
+ 13Z+: 1.02471e-002 3.81045e-004
+ 14X-: 2.27298e-002 -2.97998e-002
+ 14Y-: 6.80884e-003 -5.87749e-002
+ 14Z+: -5.60118e-002 1.22369e-002
+ 15X-: 1.58816e-002 -2.73801e-002
+ 15Y-: -4.65134e-003 -3.94529e-002
+ 15Z+: 2.50206e-003 -5.49328e-003
+ 16X-: 5.31662e-002 3.93576e-002
+ 16Y-: 3.52072e-002 3.69029e-002
+ 16Z+: 7.06422e-002 9.31811e-002
+ 17X-: 1.56076e-002 -9.08195e-004
+ 17Y-: 2.67176e-002 -4.63753e-002
+ 17Z+: -9.11931e-003 4.69589e-002
+ 18X-: 1.79448e-002 -2.63955e-002
+ 18Y-: 1.75773e-002 -5.68465e-002
+ 18Z+: -6.99810e-002 4.60104e-002
+ 19X-: 2.18228e-002 -1.65593e-002
+ 19Y-: 1.32894e-002 -2.41919e-002
+ 19Z+: 3.98547e-003 -2.28182e-002
+ 20X-: 1.64195e-002 -3.97620e-003
+ 20Y-: 9.46158e-003 -1.51407e-002
+ 20Z+: 6.58752e-002 -2.52389e-002
+ 21X-: 5.49771e-002 -9.36735e-003
+ 21Y-: -3.17583e-002 7.02613e-002
+ 21Z+: 3.88241e-002 -3.82015e-002
+ 22X-: 4.65305e-002 1.67138e-002
+ 22Y-: -2.33867e-002 4.50815e-002
+ 22Z+: -3.99041e-002 2.05210e-002
+ 23X-: 5.56056e-002 -1.90433e-002
+ 23Z+: -9.78181e-003 3.99351e-002
+ 23Y+: 1.60317e-002 -3.27307e-002
+
+Mode 14
+freq = 105.43696Hz
+damp = 3.27213%
+modal A = -8.03639e+003-7.00743e+004i
+modal B = -4.65722e+007+3.80208e+006i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 4.64151e-002 -2.90348e-003
+ 1Y-: 6.95115e-002 1.27093e-001
+ 1Z+: -2.44510e-002 3.75890e-002
+ 2X-: 4.14910e-002 -1.88104e-002
+ 2Y-: 5.04230e-002 1.30725e-001
+ 2Z+: -1.04318e-001 5.83970e-002
+ 3Y-: 4.28831e-002 1.54486e-001
+ 3X+: -2.31056e-002 3.90392e-002
+ 3Z+: -1.42159e-001 6.09971e-002
+ 4X-: 2.62014e-002 -2.75472e-002
+ 4Y-: 2.72527e-002 1.29781e-001
+ 4Z+: -9.27840e-002 3.84509e-002
+ 5X-: 1.13773e-001 1.67112e-002
+ 5Y-: 1.00824e-001 -1.40975e-001
+ 5Z+: 1.59613e-001 -4.92657e-002
+ 6X-: 7.98706e-002 5.04180e-002
+ 6Y-: -1.25530e-001 2.21832e-002
+ 6Z+: -1.34595e-001 1.43824e-001
+ 7X-: 1.34273e-001 9.85549e-003
+ 7Y-: -1.49524e-001 1.81439e-003
+ 7Z+: -2.41167e-001 4.52466e-002
+ 8X-: 9.71175e-002 8.23562e-002
+ 8Y-: -1.90008e-001 4.69449e-002
+ 8Z+: 8.49537e-002 -6.48141e-002
+ 9X-: 9.38822e-002 -1.10547e-003
+ 9Y-: -2.09458e-001 4.41919e-002
+ 9Z+: 8.22852e-002 -6.39534e-002
+ 10X-: 6.83634e-002 -1.18685e-004
+ 10Y-: -8.96997e-002 2.33511e-002
+ 10Z+: -1.10483e-001 5.45390e-002
+ 11X-: 9.95814e-002 1.19263e-002
+ 11Y-: -1.23408e-001 6.88133e-003
+ 11Z+: 3.20537e-005 5.78459e-002
+ 12X-: 1.14295e-001 1.90061e-002
+ 12Y-: -1.15883e-001 8.54782e-002
+ 12Z+: 2.66946e-001 0.00000e+000
+ 13X-: -8.90174e-003 3.19756e-002
+ 13Y-: 5.29049e-002 -1.53362e-002
+ 13Z+: 3.21427e-002 3.58936e-002
+ 14X-: 8.99977e-003 1.05599e-002
+ 14Y-: 3.89513e-002 -1.43503e-002
+ 14Z+: 2.39228e-003 4.47176e-002
+ 15X-: 9.47962e-003 4.18134e-003
+ 15Y-: 5.79678e-003 -2.37185e-002
+ 15Z+: -5.87652e-002 5.69663e-002
+ 16X-: -1.26962e-001 -2.39610e-002
+ 16Y-: -1.52792e-001 -6.26367e-002
+ 16Z+: -2.46368e-001 1.55098e-002
+ 17X-: -2.01797e-002 3.21383e-003
+ 17Y-: 1.60385e-002 -2.74679e-002
+ 17Z+: -1.31223e-002 1.45064e-002
+ 18X-: 2.14046e-002 8.13876e-003
+ 18Y-: 2.88046e-002 -1.47753e-002
+ 18Z+: -4.67402e-002 1.92424e-002
+ 19X-: -2.44484e-003 -2.40498e-003
+ 19Y-: -2.49714e-002 -1.09532e-002
+ 19Z+: -7.97849e-002 5.38559e-002
+ 20X-: -2.23666e-002 1.47050e-003
+ 20Y-: -2.17218e-002 -2.65297e-002
+ 20Z+: -9.99103e-002 1.18678e-001
+ 21X-: 1.47307e-001 7.85514e-002
+ 21Y-: -1.16286e-001 -6.27909e-002
+ 21Z+: -1.12897e-002 7.02543e-003
+ 22X-: 1.30919e-001 1.63451e-002
+ 22Y-: -7.07658e-002 -1.77217e-002
+ 22Z+: -2.08065e-001 1.00087e-001
+ 23X-: 1.76274e-001 7.85758e-002
+ 23Z+: -1.74706e-002 -7.75599e-003
+ 23Y+: 6.68081e-002 -1.40807e-002
+
+Mode 15
+freq = 106.76771Hz
+damp = 1.89158%
+modal A = 1.73222e+005+1.94075e+005i
+modal B = 1.32368e+008-1.13721e+008i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: -1.53942e-001 2.93352e-001
+ 1Y-: -3.00505e-002 -4.86249e-002
+ 1Z+: -2.91127e-002 1.29226e-002
+ 2X-: -1.98096e-001 2.04099e-001
+ 2Y-: -5.05613e-003 -7.55065e-002
+ 2Z+: -7.43778e-002 6.43991e-003
+ 3Y-: -3.88340e-002 6.41450e-002
+ 3X+: 1.75382e-001 -1.80524e-001
+ 3Z+: -4.72093e-002 9.73832e-003
+ 4X-: -1.41336e-001 2.19058e-001
+ 4Y-: -2.53477e-002 3.40751e-003
+ 4Z+: 4.92758e-003 8.12611e-004
+ 5X-: -5.33541e-002 7.10547e-002
+ 5Y-: 4.34197e-001 0.00000e+000
+ 5Z+: 6.50223e-002 9.56909e-003
+ 6X-: -1.04048e-001 7.30469e-002
+ 6Y-: 2.94239e-002 -8.12165e-002
+ 6Z+: -9.89697e-002 2.14762e-002
+ 7X-: -6.23931e-002 5.41585e-002
+ 7Y-: 3.48048e-002 -2.28548e-002
+ 7Z+: 2.58210e-002 -4.68919e-002
+ 8X-: -1.60606e-001 1.04806e-001
+ 8Y-: 1.10962e-002 -4.65213e-002
+ 8Z+: 7.35525e-003 -1.22273e-002
+ 9X-: -8.17583e-003 5.99020e-003
+ 9Y-: 1.70451e-002 -8.88819e-002
+ 9Z+: 1.63325e-002 -1.08569e-002
+ 10X-: -4.14710e-002 3.62051e-002
+ 10Y-: 1.86160e-002 -7.66165e-002
+ 10Z+: 1.77851e-002 -6.09003e-002
+ 11X-: -1.24350e-001 7.43830e-002
+ 11Y-: 2.70283e-002 -5.62940e-002
+ 11Z+: -6.58809e-002 7.41496e-002
+ 12X-: -8.84782e-002 8.72724e-002
+ 12Y-: 4.43777e-002 -2.19854e-002
+ 12Z+: -8.90671e-002 1.39827e-001
+ 13X-: -4.36067e-002 -7.82185e-003
+ 13Y-: 2.84467e-002 5.03858e-002
+ 13Z+: -5.74838e-002 3.62345e-002
+ 14X-: -2.92381e-002 -4.94817e-003
+ 14Y-: 2.20448e-002 4.44890e-002
+ 14Z+: -4.44180e-003 -2.58327e-002
+ 15X-: -1.13443e-003 -1.92278e-002
+ 15Y-: 5.28672e-002 -2.81164e-004
+ 15Z+: -5.99216e-002 1.03105e-002
+ 16X-: -1.33012e-002 -8.99119e-002
+ 16Y-: 3.18800e-002 -8.20423e-002
+ 16Z+: -9.34532e-002 -8.69142e-002
+ 17X-: -1.77355e-003 -4.29815e-002
+ 17Y-: 2.00997e-002 3.44676e-002
+ 17Z+: -2.55984e-002 -1.27145e-002
+ 18X-: -1.35262e-002 -6.93088e-003
+ 18Y-: 1.11479e-002 3.72321e-002
+ 18Z+: 3.96895e-002 -9.07582e-002
+ 19X-: 2.47832e-003 -2.75095e-002
+ 19Y-: 5.25655e-003 4.33930e-004
+ 19Z+: -3.90859e-002 -6.37843e-003
+ 20X-: 9.04073e-003 -5.02979e-002
+ 20Y-: 3.61811e-002 -1.01216e-002
+ 20Z+: -1.91522e-001 7.62906e-002
+ 21X-: -1.62500e-001 1.17819e-001
+ 21Y-: 9.27296e-002 -1.04975e-001
+ 21Z+: -1.47746e-002 -4.31240e-003
+ 22X-: -8.13119e-002 1.20753e-001
+ 22Y-: 3.58022e-002 -7.74424e-002
+ 22Z+: -2.74299e-002 -1.60631e-002
+ 23X-: -1.67912e-001 1.47687e-001
+ 23Z+: -1.55096e-002 2.96200e-002
+ 23Y+: 1.56501e-003 8.87744e-002
+
+Mode 16
+freq = 112.58508Hz
+damp = 3.02795%
+modal A = 5.46351e+003-9.46357e+003i
+modal B = -6.57437e+006-4.06578e+006i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 3.84616e-001 -5.47047e-002
+ 1Y-: 1.61494e-001 3.48847e-002
+ 1Z+: -2.45397e-002 1.51223e-002
+ 2X-: 4.49003e-001 0.00000e+000
+ 2Y-: 1.39603e-001 2.89948e-002
+ 2Z+: -1.94109e-002 2.39427e-002
+ 3Y-: 1.45104e-001 -1.98977e-002
+ 3X+: -4.24863e-001 2.02508e-002
+ 3Z+: -2.49961e-002 6.01899e-003
+ 4X-: 3.99668e-001 -4.64784e-002
+ 4Y-: 9.35603e-002 -5.41526e-003
+ 4Z+: -1.70044e-002 -1.08991e-002
+ 5X-: -5.63257e-003 8.03318e-002
+ 5Y-: 1.62931e-001 2.01666e-001
+ 5Z+: 6.04392e-002 6.26388e-003
+ 6X-: -4.04949e-002 7.75439e-002
+ 6Y-: -5.28633e-002 -1.56725e-002
+ 6Z+: -1.37969e-002 -8.55776e-004
+ 7X-: -2.96534e-002 8.64821e-002
+ 7Y-: 4.65696e-002 -1.85323e-002
+ 7Z+: -2.94748e-002 -3.59270e-002
+ 8X-: -6.25840e-002 4.61130e-002
+ 8Y-: -1.00546e-002 -6.17968e-002
+ 8Z+: -4.64751e-002 -8.91343e-005
+ 9X-: -1.11364e-002 3.42097e-002
+ 9Y-: -4.38181e-002 -1.96742e-002
+ 9Z+: 8.50411e-002 -1.36698e-003
+ 10X-: -1.46363e-002 4.84919e-002
+ 10Y-: -4.32547e-002 -1.12021e-002
+ 10Z+: -5.35452e-004 -4.92953e-002
+ 11X-: -2.06184e-002 6.06990e-002
+ 11Y-: 2.79571e-002 -4.94072e-002
+ 11Z+: -5.20522e-003 5.35482e-002
+ 12X-: 3.83461e-003 9.42319e-002
+ 12Y-: -3.99045e-002 -8.32211e-002
+ 12Z+: -3.02192e-002 9.66288e-002
+ 13X-: 1.50714e-002 -7.56798e-003
+ 13Y-: -9.39346e-003 4.18168e-003
+ 13Z+: -2.74110e-003 1.81703e-002
+ 14X-: 2.15823e-002 -9.49806e-003
+ 14Y-: -1.22912e-002 3.06223e-003
+ 14Z+: -3.38651e-002 -2.17669e-002
+ 15X-: 2.47619e-002 -1.15748e-002
+ 15Y-: -6.94744e-003 -1.36732e-002
+ 15Z+: -2.89981e-002 -6.71498e-003
+ 16X-: 6.15705e-002 -2.74533e-003
+ 16Y-: 2.25668e-002 -1.33057e-002
+ 16Z+: 1.39074e-002 2.06901e-002
+ 17X-: 3.86036e-002 -1.03318e-002
+ 17Y-: 3.05547e-003 1.03921e-002
+ 17Z+: 9.48546e-004 1.17782e-002
+ 18X-: 2.96924e-002 -4.54562e-003
+ 18Y-: -7.27756e-003 1.10553e-003
+ 18Z+: -2.53581e-002 -3.00506e-002
+ 19X-: 3.48387e-002 -4.25259e-003
+ 19Y-: -9.58240e-003 -1.15040e-002
+ 19Z+: -3.81361e-002 -2.25161e-002
+ 20X-: 3.89825e-002 -1.04642e-002
+ 20Y-: -1.01760e-003 -6.59950e-003
+ 20Z+: -5.32768e-002 2.35769e-002
+ 21X-: -1.73630e-002 9.10857e-002
+ 21Y-: -1.61536e-003 -4.11870e-002
+ 21Z+: 2.21779e-002 1.03308e-003
+ 22X-: -3.82135e-003 8.73528e-002
+ 22Y-: -1.49465e-002 -3.13248e-002
+ 22Z+: -1.39985e-002 -2.89996e-002
+ 23X-: -1.23285e-002 1.01511e-001
+ 23Z+: 5.33345e-003 1.62932e-002
+ 23Y+: 7.66760e-003 2.08641e-002
+
+Mode 17
+freq = 116.84928Hz
+damp = 2.71094%
+modal A = -2.00775e+004+5.23111e+004i
+modal B = 3.79924e+007+1.57763e+007i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: -2.19035e-001 4.50854e-002
+ 1Y-: 3.89026e-001 9.51348e-004
+ 1Z+: -2.65207e-002 -2.71542e-002
+ 2X-: -1.08818e-001 -8.29388e-002
+ 2Y-: 4.02529e-001 1.38778e-017
+ 2Z+: -4.27820e-002 -8.03898e-002
+ 3Y-: 2.92798e-001 8.92352e-002
+ 3X+: 1.86140e-001 6.49153e-002
+ 3Z+: -7.33872e-002 -8.18945e-002
+ 4X-: -2.64063e-001 -9.75742e-003
+ 4Y-: 2.61956e-001 1.28605e-001
+ 4Z+: -5.90732e-002 -3.92795e-002
+ 5X-: 5.93075e-002 2.38680e-002
+ 5Y-: 1.10012e-001 -3.55569e-002
+ 5Z+: 2.96123e-002 6.97170e-002
+ 6X-: 4.76830e-002 2.77366e-002
+ 6Y-: -2.30531e-002 -1.19733e-002
+ 6Z+: -4.22326e-002 5.46449e-002
+ 7X-: 7.42666e-002 2.81374e-002
+ 7Y-: -4.70592e-002 -7.36573e-002
+ 7Z+: -8.19562e-002 -9.64588e-002
+ 8X-: 3.79590e-002 7.45530e-002
+ 8Y-: -8.70037e-002 -2.97736e-002
+ 8Z+: 3.23832e-002 -2.75728e-002
+ 9X-: 1.71400e-002 -4.34215e-003
+ 9Y-: -8.00246e-002 -7.68835e-002
+ 9Z+: 4.26725e-002 -6.10375e-003
+ 10X-: 2.33232e-002 -2.25365e-002
+ 10Y-: -2.80699e-002 -1.33336e-002
+ 10Z+: -3.39764e-002 5.29191e-002
+ 11X-: 3.97547e-002 -2.05248e-002
+ 11Y-: -6.17298e-002 -3.65385e-002
+ 11Z+: 3.10570e-002 1.33692e-002
+ 12X-: 5.85732e-002 -7.36649e-003
+ 12Y-: -1.02934e-001 7.39063e-002
+ 12Z+: 1.28736e-001 1.19318e-001
+ 13X-: -1.11193e-002 2.06334e-002
+ 13Y-: 1.80510e-002 3.61650e-002
+ 13Z+: 2.42630e-002 4.00594e-002
+ 14X-: -7.46384e-003 8.05842e-003
+ 14Y-: 1.32625e-002 2.32131e-002
+ 14Z+: 9.10931e-003 1.01017e-001
+ 15X-: -8.63785e-003 1.24616e-002
+ 15Y-: -3.04683e-003 8.56978e-003
+ 15Z+: -9.25734e-003 2.34367e-002
+ 16X-: -2.11770e-002 -1.19046e-001
+ 16Y-: -2.58413e-002 -1.54341e-001
+ 16Z+: -1.29777e-002 -1.65042e-001
+ 17X-: -1.09973e-002 -8.93921e-003
+ 17Y-: 1.22589e-002 -1.58261e-002
+ 17Z+: 1.60570e-002 -5.10171e-003
+ 18X-: -2.74980e-003 1.26648e-002
+ 18Y-: 8.82365e-003 1.07341e-002
+ 18Z+: 3.07199e-003 6.24949e-002
+ 19X-: -6.70190e-003 -9.48015e-003
+ 19Y-: -6.33483e-003 -1.09265e-002
+ 19Z+: -2.22634e-002 2.65655e-002
+ 20X-: -1.15472e-002 -3.18392e-003
+ 20Y-: -3.26405e-003 -2.22541e-002
+ 20Z+: 6.57129e-003 3.99771e-002
+ 21X-: 6.12762e-002 6.11808e-002
+ 21Y-: -2.98906e-002 -5.14469e-002
+ 21Z+: -1.45925e-002 -1.18013e-002
+ 22X-: 7.02164e-002 7.39255e-002
+ 22Y-: -2.68467e-002 -2.64860e-002
+ 22Z+: -1.00558e-001 -4.68168e-002
+ 23X-: 7.48135e-002 7.72694e-002
+ 23Z+: -8.51818e-003 -5.66327e-002
+ 23Y+: 2.62096e-002 5.02975e-002
+
+Mode 18
+freq = 124.13356Hz
+damp = 0.56008%
+modal A = -6.04037e+004-8.70001e+004i
+modal B = -6.81189e+007+4.67313e+007i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 1.59140e-001 5.65169e-002
+ 1Y-: -3.38473e-001 -5.05125e-002
+ 1Z+: 6.40707e-002 2.42729e-002
+ 2X-: 1.03448e-001 1.64930e-001
+ 2Y-: -3.50429e-001 -6.17249e-002
+ 2Z+: 7.25120e-002 3.91734e-002
+ 3Y-: -3.15650e-001 -1.37860e-001
+ 3X+: -1.60028e-001 -1.68040e-001
+ 3Z+: 9.86981e-002 2.80624e-002
+ 4X-: 1.56340e-001 6.78739e-002
+ 4Y-: -2.90844e-001 -1.80392e-001
+ 4Z+: 7.12121e-002 2.24981e-002
+ 5X-: 4.06842e-002 2.58038e-002
+ 5Y-: 3.79898e-001 -2.77556e-017
+ 5Z+: 1.35094e-002 -2.99946e-003
+ 6X-: 3.85851e-002 2.21867e-002
+ 6Y-: 1.24664e-002 -2.83370e-002
+ 6Z+: 1.19135e-001 -1.82429e-002
+ 7X-: -8.97038e-003 2.37816e-002
+ 7Y-: 5.28131e-002 5.56896e-003
+ 7Z+: 7.09958e-002 1.98101e-003
+ 8X-: -6.14490e-004 8.70407e-003
+ 8Y-: 6.45046e-002 -1.91272e-002
+ 8Z+: -1.08249e-001 1.13925e-002
+ 9X-: -7.29723e-003 2.66463e-002
+ 9Y-: 5.93763e-002 1.01512e-002
+ 9Z+: -9.42557e-002 1.15537e-002
+ 10X-: -1.65574e-003 2.86357e-002
+ 10Y-: -4.46536e-002 -1.52381e-002
+ 10Z+: -3.97665e-003 -4.47206e-002
+ 11X-: -5.09050e-002 4.77894e-002
+ 11Y-: -1.57976e-003 -1.67962e-002
+ 11Z+: -1.80689e-002 7.38344e-003
+ 12X-: 3.16944e-002 3.58817e-002
+ 12Y-: 1.10336e-001 -6.43447e-002
+ 12Z+: -4.07788e-002 1.43930e-002
+ 13X-: 3.41152e-003 -4.61167e-003
+ 13Y-: 2.22398e-002 -1.53245e-002
+ 13Z+: -2.28905e-002 4.31394e-003
+ 14X-: -1.05061e-003 2.04005e-003
+ 14Y-: 1.58786e-002 -9.94481e-003
+ 14Z+: -5.41299e-002 -3.28376e-002
+ 15X-: 8.16291e-003 -3.09924e-003
+ 15Y-: 1.30422e-002 -1.21298e-002
+ 15Z+: -5.43424e-002 3.80838e-003
+ 16X-: -6.66173e-002 4.20385e-002
+ 16Y-: -6.35593e-002 4.01329e-002
+ 16Z+: -1.44683e-001 6.91213e-002
+ 17X-: -1.43348e-002 4.67182e-003
+ 17Y-: 1.56734e-002 4.23613e-003
+ 17Z+: -3.84956e-002 1.28937e-002
+ 18X-: 3.97584e-003 6.66668e-004
+ 18Y-: 1.52499e-002 -5.07980e-003
+ 18Z+: -8.11719e-002 -2.74120e-002
+ 19X-: -6.13390e-004 6.34448e-003
+ 19Y-: -1.38601e-002 -1.66865e-003
+ 19Z+: -4.84364e-002 -8.29309e-003
+ 20X-: -1.14133e-002 3.42986e-004
+ 20Y-: -2.31665e-003 4.49508e-004
+ 20Z+: -9.32208e-002 8.48492e-003
+ 21X-: 3.57996e-002 3.11533e-002
+ 21Y-: -5.18265e-002 -1.97251e-002
+ 21Z+: 5.07040e-002 1.05545e-002
+ 22X-: 4.94387e-002 2.63973e-003
+ 22Y-: -4.20391e-002 -9.93651e-003
+ 22Z+: 1.50597e-001 6.84551e-003
+ 23X-: 4.54423e-002 2.73938e-002
+ 23Z+: 3.46418e-002 2.26216e-002
+ 23Y+: 4.63715e-002 -1.44133e-002
+
+Mode 19
+freq = 145.35893Hz
+damp = 1.64638%
+modal A = 1.50266e+004-1.61655e+005i
+modal B = -1.47397e+008-1.61530e+007i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: -5.60027e-002 1.41332e-001
+ 1Y-: 9.98561e-002 -1.48311e-001
+ 1Z+: -1.30559e-002 1.57592e-001
+ 2X-: -2.93807e-002 7.96200e-002
+ 2Y-: 1.09693e-001 -1.71510e-001
+ 2Z+: -3.55417e-002 1.14960e-001
+ 3Y-: 7.46069e-002 -9.97644e-002
+ 3X+: 5.47355e-002 -8.44193e-002
+ 3Z+: -2.05433e-002 7.19150e-002
+ 4X-: -7.56769e-002 1.54880e-001
+ 4Y-: 1.25717e-001 -1.64834e-001
+ 4Z+: -1.25132e-002 8.68357e-002
+ 5X-: -1.88315e-002 1.38157e-001
+ 5Y-: 2.86666e-001 8.67362e-019
+ 5Z+: 4.06099e-002 1.31455e-001
+ 6X-: -5.49448e-002 1.24633e-001
+ 6Y-: 1.01642e-003 -8.86310e-002
+ 6Z+: -1.16446e-001 9.76899e-002
+ 7X-: -1.25484e-004 1.14776e-001
+ 7Y-: 1.80206e-002 -5.16840e-002
+ 7Z+: 1.45578e-003 -1.34548e-001
+ 8X-: -1.01579e-001 1.50599e-001
+ 8Y-: -4.34082e-002 -6.43978e-002
+ 8Z+: 5.42656e-002 -1.90610e-002
+ 9X-: -3.80577e-002 4.61290e-003
+ 9Y-: 8.36759e-002 2.82838e-002
+ 9Z+: -1.35775e-002 -1.83384e-001
+ 10X-: -2.11105e-003 1.97515e-002
+ 10Y-: 2.87102e-002 -1.36048e-001
+ 10Z+: 1.38958e-002 -4.71938e-002
+ 11X-: -1.94009e-002 9.16880e-002
+ 11Y-: 2.79451e-002 -1.35771e-001
+ 11Z+: 2.67280e-002 3.15566e-002
+ 12X-: -1.32393e-002 1.82559e-001
+ 12Y-: -7.49389e-003 5.76521e-002
+ 12Z+: -1.07501e-001 3.82139e-002
+ 13X-: -1.25688e-002 6.71201e-002
+ 13Y-: 6.96336e-003 2.90630e-002
+ 13Z+: 5.49382e-003 5.97130e-002
+ 14X-: -1.80475e-002 3.43799e-002
+ 14Y-: 6.42766e-003 1.73134e-002
+ 14Z+: 1.50308e-002 1.40718e-002
+ 15X-: -8.30116e-003 1.82514e-002
+ 15Y-: 1.58298e-002 -3.34831e-002
+ 15Z+: -1.00859e-002 -7.99415e-003
+ 16X-: 5.27228e-002 -1.00061e-001
+ 16Y-: 7.20416e-002 -1.95613e-001
+ 16Z+: 1.08550e-001 -1.69994e-001
+ 17X-: 8.19809e-003 6.29907e-003
+ 17Y-: 2.60021e-002 -9.62521e-003
+ 17Z+: 4.60087e-002 -1.63539e-003
+ 18X-: -1.26461e-002 4.43311e-002
+ 18Y-: 9.31238e-003 6.94062e-003
+ 18Z+: 4.72749e-002 -6.04304e-002
+ 19X-: 3.30179e-003 5.56430e-003
+ 19Y-: 1.78721e-002 -4.14950e-002
+ 19Z+: -2.72084e-002 -3.55754e-002
+ 20X-: 1.82274e-002 -6.61396e-003
+ 20Y-: 3.23255e-002 -5.77882e-002
+ 20Z+: 2.08254e-002 4.44716e-002
+ 21X-: -8.37603e-002 2.24427e-001
+ 21Y-: 5.64132e-002 -1.24615e-001
+ 21Z+: -3.05985e-002 8.60014e-002
+ 22X-: -4.56534e-002 1.92277e-001
+ 22Y-: 1.77195e-002 -6.49236e-002
+ 22Z+: -9.57913e-002 -2.59563e-002
+ 23X-: -8.43398e-002 2.60706e-001
+ 23Z+: 7.74429e-004 6.45601e-002
+ 23Y+: -1.05880e-002 6.10895e-002
+
+Mode 20
+freq = 150.10734Hz
+damp = 2.17368%
+modal A = 1.66427e+005+1.73772e+005i
+modal B = 1.67266e+008-1.53366e+008i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 2.43779e-003 -1.71297e-002
+ 1Y-: 4.73042e-002 1.32390e-001
+ 1Z+: -4.71249e-002 -5.12540e-002
+ 2X-: 1.90969e-002 -1.33459e-002
+ 2Y-: 4.75174e-002 1.32134e-001
+ 2Z+: -5.59745e-002 -7.24343e-002
+ 3Y-: 2.16856e-002 1.30177e-001
+ 3X+: -4.25826e-004 4.90038e-002
+ 3Z+: -4.55806e-002 -7.39268e-002
+ 4X-: -4.43028e-003 -2.59985e-002
+ 4Y-: 3.50546e-002 1.20607e-001
+ 4Z+: -3.60346e-002 -5.20821e-002
+ 5X-: -2.72515e-003 2.65511e-002
+ 5Y-: 3.82266e-001 0.00000e+000
+ 5Z+: 5.18599e-002 3.65726e-002
+ 6X-: -8.84237e-003 3.38643e-002
+ 6Y-: -3.12426e-003 -7.60252e-002
+ 6Z+: -8.03074e-003 -5.18430e-002
+ 7X-: 2.35754e-004 4.93864e-002
+ 7Y-: -1.39288e-002 -1.04535e-001
+ 7Z+: -4.52585e-003 -7.35294e-002
+ 8X-: -8.09330e-002 1.70940e-002
+ 8Y-: -5.74116e-002 -1.43276e-001
+ 8Z+: -1.38717e-003 3.68941e-002
+ 9X-: -1.79788e-002 -6.57705e-003
+ 9Y-: 7.28532e-002 -2.72016e-002
+ 9Z+: 9.40608e-002 1.65348e-001
+ 10X-: -1.98154e-002 -2.54428e-002
+ 10Y-: -9.42107e-002 -2.60846e-001
+ 10Z+: -4.61862e-002 -1.72115e-001
+ 11X-: -3.31184e-002 3.13332e-002
+ 11Y-: -1.19648e-001 -3.18029e-001
+ 11Z+: -1.78480e-001 -3.24369e-001
+ 12X-: 3.11212e-002 4.25169e-002
+ 12Y-: -1.34896e-002 -8.88806e-002
+ 12Z+: 3.29458e-002 1.19113e-001
+ 13X-: -5.24058e-003 5.60663e-003
+ 13Y-: 3.85149e-002 3.85674e-002
+ 13Z+: 1.04633e-001 1.02772e-001
+ 14X-: -8.00215e-003 8.76095e-003
+ 14Y-: 3.44992e-002 3.67628e-002
+ 14Z+: -9.51863e-003 2.76250e-002
+ 15X-: 5.18735e-003 6.78402e-003
+ 15Y-: 3.93851e-002 2.36532e-002
+ 15Z+: -9.44307e-002 -5.39743e-002
+ 16X-: 3.95350e-002 2.32162e-002
+ 16Y-: 6.16057e-002 9.75588e-003
+ 16Z+: 1.53273e-001 1.20582e-001
+ 17X-: 2.12578e-002 2.75781e-002
+ 17Y-: 6.35242e-002 5.15130e-002
+ 17Z+: 1.42791e-001 1.41492e-001
+ 18X-: 2.38478e-003 2.01321e-002
+ 18Y-: 5.57283e-002 5.57094e-002
+ 18Z+: -6.95583e-003 1.88998e-002
+ 19X-: 1.24551e-002 1.50428e-002
+ 19Y-: 4.53742e-002 4.24108e-002
+ 19Z+: -1.56612e-001 -1.52638e-001
+ 20X-: 3.41276e-002 3.62056e-002
+ 20Y-: 6.06514e-002 4.21505e-002
+ 20Z+: 6.68460e-002 1.17220e-001
+ 21X-: -3.75561e-002 3.37291e-002
+ 21Y-: 1.46833e-003 -8.38924e-002
+ 21Z+: 2.25130e-002 -1.56436e-002
+ 22X-: -1.02525e-002 4.87003e-002
+ 22Y-: -1.96867e-002 -8.21470e-002
+ 22Z+: 1.68703e-002 -6.27926e-002
+ 23X-: -3.89762e-002 4.44931e-002
+ 23Z+: 8.51820e-003 -7.14570e-003
+ 23Y+: 1.92463e-002 7.79396e-002
+
+Mode 21
+freq = 164.65885Hz
+damp = 1.39142%
+modal A = -2.41033e+005+2.81618e+005i
+modal B = 2.87859e+008+2.53398e+008i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: 3.50861e-002 -2.19931e-002
+ 1Y-: -7.16977e-002 -2.04598e-002
+ 1Z+: 2.92012e-002 -1.25382e-002
+ 2X-: 3.19810e-002 -1.43584e-002
+ 2Y-: -8.00415e-002 -2.25942e-002
+ 2Z+: 5.63089e-002 6.06573e-003
+ 3Y-: -7.26208e-002 -2.13908e-002
+ 3X+: -4.29234e-002 6.98265e-003
+ 3Z+: 4.75277e-002 2.62996e-002
+ 4X-: 3.40086e-002 -2.24185e-002
+ 4Y-: -5.70973e-002 -1.29427e-002
+ 4Z+: 1.61911e-002 4.98311e-003
+ 5X-: -1.84045e-002 -3.79862e-002
+ 5Y-: 1.34920e-002 -2.13017e-001
+ 5Z+: -8.56236e-003 -3.10474e-002
+ 6X-: -1.28128e-002 -1.47459e-002
+ 6Y-: 5.50841e-002 1.21362e-002
+ 6Z+: 9.51668e-002 2.81070e-003
+ 7X-: -4.44054e-002 -4.02699e-002
+ 7Y-: 5.55706e-002 -2.09976e-004
+ 7Z+: 1.91526e-002 2.45270e-002
+ 8X-: 1.28732e-003 1.23168e-002
+ 8Y-: 8.37346e-002 3.99176e-002
+ 8Z+: -3.23238e-002 2.40723e-002
+ 9X-: -2.17623e-002 -1.77784e-002
+ 9Y-: 3.00754e-002 2.70035e-002
+ 9Z+: -4.11723e-002 1.48332e-002
+ 10X-: 7.11608e-002 9.83590e-003
+ 10Y-: 3.99240e-001 6.35974e-002
+ 10Z+: 3.25644e-001 3.90991e-002
+ 11X-: -2.34831e-002 9.25893e-003
+ 11Y-: 4.56240e-001 7.80094e-002
+ 11Z+: 4.81365e-001 0.00000e+000
+ 12X-: 6.92362e-003 -1.21448e-002
+ 12Y-: 1.19187e-001 5.12997e-002
+ 12Z+: -3.12677e-002 -1.40030e-002
+ 13X-: 3.25489e-002 1.88661e-002
+ 13Y-: 1.48974e-002 1.36472e-002
+ 13Z+: 6.21421e-002 5.78920e-002
+ 14X-: 1.96402e-003 1.05830e-002
+ 14Y-: 4.87782e-003 1.25245e-002
+ 14Z+: -3.97379e-002 -2.53172e-002
+ 15X-: 1.23055e-002 1.01995e-002
+ 15Y-: 2.96664e-003 1.58193e-002
+ 15Z+: -7.07192e-002 -5.80739e-002
+ 16X-: -2.47336e-003 1.41266e-002
+ 16Y-: 1.77344e-003 2.77450e-002
+ 16Z+: 6.16527e-002 7.91265e-002
+ 17X-: 1.52142e-002 2.27048e-002
+ 17Y-: 2.56495e-002 2.88367e-002
+ 17Z+: 9.02655e-002 1.06442e-001
+ 18X-: 1.47944e-002 1.75665e-002
+ 18Y-: 3.67090e-002 4.39057e-002
+ 18Z+: -6.64044e-002 -4.85581e-002
+ 19X-: 6.54482e-003 9.72706e-003
+ 19Y-: 2.83197e-002 4.87456e-002
+ 19Z+: -1.16460e-001 -1.38545e-001
+ 20X-: 1.27102e-002 2.25280e-002
+ 20Y-: 2.12515e-002 3.73299e-002
+ 20Z+: 6.11394e-002 6.56215e-002
+ 21X-: -2.34249e-003 -2.68757e-002
+ 21Y-: 5.40329e-002 3.22775e-002
+ 21Z+: 4.07525e-002 1.08185e-002
+ 22X-: -1.88091e-002 -4.26278e-002
+ 22Y-: 6.10286e-002 3.63879e-002
+ 22Z+: 8.43691e-002 5.31388e-002
+ 23X-: -6.61190e-003 -3.26827e-002
+ 23Z+: 1.62616e-002 1.18004e-002
+ 23Y+: -5.82587e-002 -3.37040e-002
diff --git a/modal-analysis/mat/nohup.out b/modal-analysis/mat/nohup.out
new file mode 100644
index 0000000..c749eee
--- /dev/null
+++ b/modal-analysis/mat/nohup.out
@@ -0,0 +1,2 @@
+
+(termite:6464): GLib-WARNING **: 10:26:13.129: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.
diff --git a/modal-analysis/mathematical_model.org b/modal-analysis/mathematical_model.org
index e73859b..f4e45eb 100644
--- a/modal-analysis/mathematical_model.org
+++ b/modal-analysis/mathematical_model.org
@@ -7,7 +7,7 @@
#+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html
-#+HTML_LINK_UP: ../index.html
+#+HTML_LINK_UP: ./index.html
#+HTML_HEAD:
#+HTML_HEAD:
@@ -38,3 +38,25 @@
#+PROPERTY: header-args:latex+ :mkdirp yes
#+PROPERTY: header-args:latex+ :output-dir figs
:END:
+
+* Type of Model
+The model that we want to obtain is a *multi-body model*.
+It is composed of several *solid bodies connected with springs and dampers*.
+The solid bodies are represented with different colors on figure [[fig:nass_solidworks]].
+
+In the simscape model, the solid bodies are:
+- the granite (1 or 2 solids)
+- the translation stage
+- the tilt stage
+- the spindle and slip-ring
+- the hexapod
+
+#+name: fig:nass_solidworks
+#+caption: CAD view of the ID31 Micro-Station
+#+attr_html: :width 800px
+[[file:img/nass_solidworks.png]]
+
+However, each of the DOF of the system may not be relevant for the modes present in the frequency band of interest.
+For instance, the translation stage may not vibrate in the Z direction for all the modes identified. Then, we can block this DOF and this simplifies the model.
+
+The modal identification done here will thus permit us to determine *which DOF can be neglected*.
diff --git a/modal-analysis/matlab/modal_frf_coh.m b/modal-analysis/matlab/modal_frf_coh.m
new file mode 100644
index 0000000..7960cf3
--- /dev/null
+++ b/modal-analysis/matlab/modal_frf_coh.m
@@ -0,0 +1,317 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+% Windowing
+% Windowing is used on the force and response signals.
+
+% A boxcar window (figure [[fig:windowing_force_signal]]) is used for the force signal as once the impact on the structure is done, the measured signal is meaningless.
+% The parameters are:
+% - *Start*: $3\%$
+% - *Stop*: $7\%$
+
+
+figure;
+plot(100*[0, 0.03, 0.03, 0.07, 0.07, 1], [0, 0, 1, 1, 0, 0]);
+xlabel('Time [%]'); ylabel('Amplitude');
+xlim([0, 100]); ylim([0, 1]);
+
+
+
+% #+NAME: fig:windowing_force_signal
+% #+CAPTION: Window used for the force signal
+% [[file:figs/windowing_force_signal.png]]
+
+% An exponential window (figure [[fig:windowing_response_signal]]) is used for the response signal as we are measuring transient signals and most of the information is located at the beginning of the signal.
+% The parameters are:
+% - FlatTop:
+% - *Start*: $3\%$
+% - *Stop*: $2.96\%$
+% - Decreasing point:
+% - *X*: $60.4\%$
+% - *Y*: $14.7\%$
+
+
+x0 = 0.296;
+xd = 0.604;
+yd = 0.147;
+
+alpha = log(yd)/(x0 - xd);
+
+t = x0:0.01:1.01;
+y = exp(-alpha*(t-x0));
+
+figure;
+plot(100*[0, 0.03, 0.03, x0, t], [0, 0, 1, 1, y]);
+xlabel('Time [%]'); ylabel('Amplitude');
+xlim([0, 100]); ylim([0, 1]);
+
+% Force and Response signals
+% Let's load some obtained data to look at the force and response signals.
+
+
+meas1_raw = load('mat/meas_raw_1.mat');
+
+% Raw Force Data
+% The force input for the first measurement is shown on figure [[fig:raw_data_force]]. We can see 10 impacts, one zoom on one impact is shown on figure [[fig:raw_data_force_zoom]].
+
+% The Fourier transform of the force is shown on figure [[fig:fourier_transfor_force_impact]]. This has been obtained without any windowing.
+
+
+time = linspace(0, meas1_raw.Track1_X_Resolution*length(meas1_raw.Track1), length(meas1_raw.Track1));
+
+figure;
+plot(time, meas1_raw.Track1);
+xlabel('Time [s]');
+ylabel('Force [N]');
+
+
+
+% #+NAME: fig:raw_data_force
+% #+CAPTION: Raw Force Data from Hammer Blow
+% [[file:figs/raw_data_force.png]]
+
+
+figure;
+plot(time, meas1_raw.Track1);
+xlabel('Time [s]');
+ylabel('Force [N]');
+xlim([22.1, 22.3]);
+
+
+
+% #+NAME: fig:raw_data_force_zoom
+% #+CAPTION: Raw Force Data from Hammer Blow - Zoom
+% [[file:figs/raw_data_force_zoom.png]]
+
+
+Fs = 1/meas1_raw.Track1_X_Resolution; % Sampling Frequency [Hz]
+impacts = [5.9, 11.2, 16.6, 22.2, 27.3, 32.7, 38.1, 43.8, 50.4]; % Time just before the impact occurs [s]
+
+L = 8194;
+f = Fs*(0:(L/2))/L; % Frequency vector [Hz]
+
+F_fft = zeros((8193+1)/2+1, length(impacts));
+
+for i = 1:length(impacts)
+ t0 = impacts(i);
+ [~, i_start] = min(abs(time-t0));
+ i_end = i_start + 8193;
+
+ Y = fft(meas1_raw.Track1(i_start:i_end));
+
+ P2 = abs(Y/L);
+ P1 = P2(1:L/2+1);
+ P1(2:end-1) = 2*P1(2:end-1);
+ F_fft(:, i) = P1;
+end
+
+figure;
+hold on;
+for i = 1:length(impacts)
+ plot(f, F_fft(:, i), '-k');
+end
+hold off;
+xlim([0, 200]);
+xlabel('Frequency [Hz]'); ylabel('Force [N]');
+
+% Raw Response Data
+% The response signal for the first measurement is shown on figure [[fig:raw_data_acceleration]]. One zoom on one response is shown on figure [[fig:raw_data_acceleration_zoom]].
+
+% The Fourier transform of the response signals is shown on figure [[fig:fourier_transform_response_signals]]. This has been obtained without any windowing.
+
+
+figure;
+plot(time, meas1_raw.Track2);
+xlabel('Time [s]');
+ylabel('Acceleration [m/s2]');
+
+
+
+% #+NAME: fig:raw_data_acceleration
+% #+CAPTION: Raw Acceleration Data from Accelerometer
+% [[file:figs/raw_data_acceleration.png]]
+
+
+figure;
+plot(time, meas1_raw.Track2);
+xlabel('Time [s]');
+ylabel('Acceleration [m/s2]');
+xlim([22.1, 22.5]);
+
+
+
+% #+NAME: fig:raw_data_acceleration_zoom
+% #+CAPTION: Raw Acceleration Data from Accelerometer - Zoom
+% [[file:figs/raw_data_acceleration_zoom.png]]
+
+
+X_fft = zeros((8193+1)/2+1, length(impacts));
+
+for i = 1:length(impacts)
+ t0 = impacts(i);
+ [~, i_start] = min(abs(time-t0));
+ i_end = i_start + 8193;
+
+ Y = fft(meas1_raw.Track2(i_start:i_end));
+
+ P2 = abs(Y/L);
+ P1 = P2(1:L/2+1);
+ P1(2:end-1) = 2*P1(2:end-1);
+ X_fft(:, i) = P1;
+end
+
+figure;
+hold on;
+for i = 1:length(impacts)
+ plot(f, X_fft(:, i), '-k');
+end
+hold off;
+xlim([0, 200]);
+set(gca, 'Yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Acceleration [$m/s^2$]');
+
+% Computation of one Frequency Response Function
+% Now that we have obtained the Fourier transform of both the force input and the response signal, we can compute the Frequency Response Function from the force to the acceleration.
+
+% We then compare the result obtained with the FRF computed by the modal software (figure [[fig:frf_comparison_software]]).
+
+% The slight difference can probably be explained by the use of windows.
+
+% In the following analysis, FRF computed from the software will be used.
+
+
+meas1 = load('mat/meas_frf_coh_1.mat');
+
+figure;
+hold on;
+for i = 1:length(impacts)
+ plot(f, X_fft(:, i)./F_fft(:, i), '-k');
+end
+plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvSpc_2_RMS_Y_Val)
+hold off;
+xlim([0, 200]);
+set(gca, 'Yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Acceleration/Force [$m/s^2/N$]');
+
+% Frequency Response Functions and Coherence Results
+% Let's see one computed Frequency Response Function and one coherence in order to attest the quality of the measurement.
+
+% First, we load the data.
+
+meas1 = load('mat/meas_frf_coh_1.mat');
+
+
+
+% And we plot on figure [[fig:frf_result_example]] the frequency response function from the force applied in the $X$ direction at the location of the accelerometer number 11 to the acceleration in the $X$ direction as measured by the first accelerometer located on the top platform of the hexapod.
+
+% The coherence associated is shown on figure [[fig:frf_result_example]].
+
+
+figure;
+ax1 = subplot(2, 1, 1);
+plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvXSpc_2_1_RMS_Y_Mod);
+set(gca, 'Yscale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Magnitude');
+
+ax2 = subplot(2, 1, 2);
+plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvXSpc_2_1_RMS_Y_Phas);
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:frf_result_example
+% #+CAPTION: Example of one measured FRF
+% [[file:figs/frf_result_example.png]]
+
+
+figure;
+plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_Coh_2_1_RMS_Y_Val);
+xlabel('Frequency [Hz]');
+ylabel('Coherence');
+
+% Generation of a FRF matrix and a Coherence matrix from the measurements
+% We want here to combine all the Frequency Response Functions measured into one big array called the *Frequency Response Matrix*.
+
+% The frequency response matrix is an $n \times p \times q$:
+% - $n$ is the number of measurements: $23 \times 3$ (23 accelerometers measuring 3 directions each)
+% - $p$ is the number of excitation inputs: $3$
+% - $q$ is the number of frequency points $\omega_i$
+
+% Thus, the FRF matrix is an $69 \times 3 \times 801$ matrix.
+
+
+% #+begin_important
+% For each frequency point $\omega_i$, we obtain a 2D matrix:
+% \begin{equation}
+% \text{FRF}(\omega_i) = \begin{bmatrix}
+% \frac{D_{1_x}}{F_x}(\omega_i) & \frac{D_{1_x}}{F_y}(\omega_i) & \frac{D_{1_x}}{F_z}(\omega_i) \\
+% \frac{D_{1_y}}{F_x}(\omega_i) & \frac{D_{1_y}}{F_y}(\omega_i) & \frac{D_{1_y}}{F_z}(\omega_i) \\
+% \frac{D_{1_z}}{F_x}(\omega_i) & \frac{D_{1_z}}{F_y}(\omega_i) & \frac{D_{1_z}}{F_z}(\omega_i) \\
+% \frac{D_{2_x}}{F_x}(\omega_i) & \frac{D_{2_x}}{F_y}(\omega_i) & \frac{D_{2_x}}{F_z}(\omega_i) \\
+% \vdots & \vdots & \vdots \\
+% \frac{D_{23_z}}{F_x}(\omega_i) & \frac{D_{23_z}}{F_y}(\omega_i) & \frac{D_{23_z}}{F_z}(\omega_i) \\
+% \end{bmatrix}
+% \end{equation}
+% #+end_important
+
+% We generate such FRF matrix from the measurements using the following script.
+
+n_meas = 24;
+n_acc = 23;
+
+dirs = 'XYZ';
+
+% Number of Accelerometer * DOF for each acccelerometer / Number of excitation / frequency points
+FRFs = zeros(3*n_acc, 3, 801);
+COHs = zeros(3*n_acc, 3, 801);
+
+% Loop through measurements
+for i = 1:n_meas
+ % Load the measurement file
+ meas = load(sprintf('mat/meas_frf_coh_%i.mat', i));
+
+ % First: determine what is the exitation (direction and sign)
+ exc_dir = meas.FFT1_AvXSpc_2_1_RMS_RfName(end);
+ exc_sign = meas.FFT1_AvXSpc_2_1_RMS_RfName(end-1);
+ % Determine what is the correct excitation sign
+ exc_factor = str2num([exc_sign, '1']);
+ if exc_dir ~= 'Z'
+ exc_factor = exc_factor*(-1);
+ end
+
+ % Then: loop through the nine measurements and store them at the correct location
+ for j = 2:10
+ % Determine what is the accelerometer and direction
+ [indices_acc_i] = strfind(meas.(sprintf('FFT1_H1_%i_1_RpName', j)), '.');
+ acc_i = str2num(meas.(sprintf('FFT1_H1_%i_1_RpName', j))(indices_acc_i(1)+1:indices_acc_i(2)-1));
+
+ meas_dir = meas.(sprintf('FFT1_H1_%i_1_RpName', j))(end);
+ meas_sign = meas.(sprintf('FFT1_H1_%i_1_RpName', j))(end-1);
+ % Determine what is the correct measurement sign
+ meas_factor = str2num([meas_sign, '1']);
+ if meas_dir ~= 'Z'
+ meas_factor = meas_factor*(-1);
+ end
+
+ % FRFs(acc_i+n_acc*(find(dirs==meas_dir)-1), find(dirs==exc_dir), :) = exc_factor*meas_factor*meas.(sprintf('FFT1_H1_%i_1_Y_ReIm', j));
+ % COHs(acc_i+n_acc*(find(dirs==meas_dir)-1), find(dirs==exc_dir), :) = meas.(sprintf('FFT1_Coh_%i_1_RMS_Y_Val', j));
+
+ FRFs(find(dirs==meas_dir)+3*(acc_i-1), find(dirs==exc_dir), :) = exc_factor*meas_factor*meas.(sprintf('FFT1_H1_%i_1_Y_ReIm', j));
+ COHs(find(dirs==meas_dir)+3*(acc_i-1), find(dirs==exc_dir), :) = meas.(sprintf('FFT1_Coh_%i_1_RMS_Y_Val', j));
+ end
+end
+freqs = meas.FFT1_Coh_10_1_RMS_X_Val;
+
+
+
+% And we save the obtained FRF matrix and Coherence matrix in a =.mat= file.
+
+save('./mat/frf_coh_matrices.mat', 'FRFs', 'COHs', 'freqs');
diff --git a/modal-analysis/measurement.html b/modal-analysis/measurement.html
index e373cd8..9b939f4 100644
Binary files a/modal-analysis/measurement.html and b/modal-analysis/measurement.html differ
diff --git a/modal-analysis/measurement.org b/modal-analysis/measurement.org
index f2b50d3..1d83081 100644
--- a/modal-analysis/measurement.org
+++ b/modal-analysis/measurement.org
@@ -7,7 +7,7 @@
#+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html
-#+HTML_LINK_UP: ../index.html
+#+HTML_LINK_UP: ./index.html
#+HTML_HEAD:
#+HTML_HEAD:
@@ -25,58 +25,40 @@
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs
+#+PROPERTY: header-args:matlab+ :tangle matlab/modal_frf_coh.m
+#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:shell :eval no-export
:END:
-* Goal
-The goal is to experimentally extract a *Spatial Model* (mass, damping, stiffness) of the structure (shown on figure [[fig:nass_picture]]) in order to tune the Multi-Body model.
+* ZIP file containing the data and matlab files :ignore:
+#+begin_src bash :exports none :results none
+ if [ matlab/modal_frf_coh.m -nt data/modal_frf_coh.zip ]; then
+ cp matlab/modal_frf_coh.m modal_frf_coh.m;
+ zip data/modal_frf_coh \
+ mat/meas_raw_1.mat \
+ mat/meas_frf_coh_*.mat \
+ mat/id31_nanostation.cfg \
+ modal_frf_coh.m
+ rm modal_frf_coh.m;
+ fi
+#+end_src
-#+name: fig:nass_picture
-#+caption: Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass
-#+attr_html: :width 500px
-[[file:img/nass_picture.png]]
+#+begin_note
+ All the files (data and Matlab scripts) are accessible [[file:data/modal_frf_coh.zip][here]].
+#+end_note
-The procedure is represented on figure [[fig:vibration_analysis_procedure]] where we go from left to right.
+* Matlab Init :noexport:ignore:
+#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
+ <>
+#+end_src
-#+name: fig:vibration_analysis_procedure
-#+caption: Vibration Analysis Procedure
-#+attr_html: :width 400px
-[[file:img/vibration_analysis_procedure.png]]
-
-First, we obtain a *Response Model* (Frequency Response Functions) from measurements.
-This is further converted into a *Modal Model* (Natural Frequencies and Mode Shapes).
-Finally, this is converted into a *Spatial Model* with the Mass/Damping/Stiffness matrices.
-
-
-Theses matrices will be used to tune the Simscape (multi-body) model.
-
-The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
-
-* Type of Model
-The model that we want to obtain is a *multi-body model*.
-It is composed of several *solid bodies connected with springs and dampers*.
-The solid bodies are represented with different colors on figure [[fig:nass_solidworks]].
-
-In the simscape model, the solid bodies are:
-- the granite (1 or 2 solids)
-- the translation stage
-- the tilt stage
-- the spindle and slip-ring
-- the hexapod
-
-#+name: fig:nass_solidworks
-#+caption: CAD view of the ID31 Micro-Station
-#+attr_html: :width 800px
-[[file:img/nass_solidworks.png]]
-
-However, each of the DOF of the system may not be relevant for the modes present in the frequency band of interest.
-For instance, the translation stage may not vibrate in the Z direction for all the modes identified. Then, we can block this DOF and this simplifies the model.
-
-The modal identification done here will thus permit us to determine *which DOF can be neglected*.
+#+begin_src matlab :exports none :results silent :noweb yes
+ <>
+#+end_src
* Instrumentation Used
-In order to perform to Modal Analysis and to obtain first a Response Model, the following devices are used:
+In order to perform to *Modal Analysis* and to obtain first a *Response Model*, the following devices are used:
- An *acquisition system* (OROS) with 24bits ADCs (figure [[fig:oros]])
- 3 tri-axis *Accelerometers* (figure [[fig:accelero_M393B05]]) with parameters shown on table [[tab:accelero_M393B05]]
- An *Instrumented Hammer* with various Tips (figure [[fig:instrumented_hammer]]) (figure [[fig:hammer_tips]])
@@ -170,9 +152,15 @@ The position of the accelerometers are:
- 4 on the second granite (figure [[fig:accelerometers_granite2_overview]])
- 4 on top of the translation stage (figure [[fig:accelerometers_ty_overview]])
- 4 on top of the tilt stage
-- 4 on top of the spindle
+- 3 on top of the spindle
- 4 on top of the hexapod (figure [[fig:accelerometers_hexa_overview]])
+In total, 23 accelerometers are used: *69 DOFs are thus measured*.
+
+The position and orientation of all the accelerometers used are shown on figure [[fig:nass-modal-test]].
+
+The precise determination of the position of each accelerometer is done using the SolidWorks model (shown on figure [[fig:location_accelerometers]]).
+
#+name: fig:accelerometers_granite2_overview
#+caption: Accelerometers located on the top granite
#+attr_html: :width 500px
@@ -188,11 +176,58 @@ The position of the accelerometers are:
#+attr_html: :width 500px
[[file:img/accelerometers/accelerometers_hexa_overview.jpg]]
+#+name: fig:nass-modal-test
+#+caption: Position and orientation of the accelerometer used
+#+attr_html: :width 800px
+[[file:figs/nass-modal-test.png]]
+
+#+name: fig:location_accelerometers
+#+caption: Position of the accelerometers using SolidWorks
+#+attr_html: :width 800px
+[[file:img/location_accelerometers.png]]
+
+The precise position of all the 23 accelerometer with respect to a frame located at the point of interest (located 270mm above the top platform of the hexapod) is shown below. The values are in meter.
+They are contained in the =mat/id31_nanostation.cfg= file.
+
+#+begin_src bash :exports results :eval no-export :post addhdr(*this*)
+ echo " ID X[m] Y[m] Z[m]"
+ cat mat/id31_nanostation.cfg | grep NODES -A 23 | sed '/\s\+[0-9]\+/!d' | sed 's/\(.*\)\s\+0\s\+.\+/\1/' | tac --
+#+end_src
+
+#+RESULTS:
+| ID | X[m] | Y[m] | Z[m] |
+|----+--------------+--------------+--------------|
+| 1 | -6.4000e-002 | -6.4000e-002 | -2.7000e-001 |
+| 2 | -6.4000e-002 | 6.4000e-002 | -2.7000e-001 |
+| 3 | 6.4000e-002 | 6.4000e-002 | -2.7000e-001 |
+| 4 | 6.4000e-002 | -6.4000e-002 | -2.7000e-001 |
+| 5 | -3.8500e-001 | -3.0000e-001 | -4.1680e-001 |
+| 6 | -4.2000e-001 | 2.8000e-001 | -4.1680e-001 |
+| 7 | 4.2000e-001 | 2.8000e-001 | -4.1680e-001 |
+| 8 | 3.8000e-001 | -3.0000e-001 | -4.1680e-001 |
+| 9 | -4.7500e-001 | -4.1400e-001 | -4.2730e-001 |
+| 10 | -4.6500e-001 | 4.0700e-001 | -4.2730e-001 |
+| 11 | 4.7500e-001 | 4.2400e-001 | -4.2730e-001 |
+| 12 | 4.7500e-001 | -4.1900e-001 | -4.2730e-001 |
+| 13 | -3.2000e-001 | -4.4600e-001 | -7.8560e-001 |
+| 14 | -4.8000e-001 | 5.3400e-001 | -7.8560e-001 |
+| 15 | 4.5000e-001 | 5.3400e-001 | -7.8560e-001 |
+| 16 | 2.9500e-001 | -4.8100e-001 | -7.8560e-001 |
+| 17 | -7.3000e-001 | -5.2600e-001 | -9.5060e-001 |
+| 18 | -7.3500e-001 | 8.1400e-001 | -9.5060e-001 |
+| 19 | 8.7500e-001 | 7.9900e-001 | -9.5060e-001 |
+| 20 | 8.6490e-001 | -5.0600e-001 | -9.5060e-001 |
+| 21 | -1.5500e-001 | -9.0000e-002 | -5.9400e-001 |
+| 22 | 0.0000e+000 | 1.8000e-001 | -5.9400e-001 |
+| 23 | 1.5500e-001 | -9.0000e-002 | -5.9400e-001 |
+
** Hammer Impacts
Only 3 impact points are used.
The impact points are shown on figures [[fig:hammer_x]], [[fig:hammer_y]] and [[fig:hammer_z]].
+We chose this excitation point as it seems to excite all the modes in the frequency band of interest and because it provides good coherence for all the accelerometers.
+
#+name: fig:hammer_x
#+caption: Hammer Blow in the X direction
#+attr_html: :width 300px
@@ -209,47 +244,93 @@ The impact points are shown on figures [[fig:hammer_x]], [[fig:hammer_y]] and [[
[[file:img/impacts/hammer_z.gif]]
* Signal Processing
-The measurements are averaged 10 times (figure [[fig:general_parameters]]) corresponding to 10 hammer impacts.
+** Averaging
+The measurements are averaged 10 times corresponding to 10 hammer impacts in order to reduce the effect of random noise.
+The parameters for the impact test are shown on table [[tab:meas_parameters]].
-#+name: fig:general_parameters
-#+caption: General Acquisition Settings
-#+attr_html: :width 500px
-[[file:img/parameters/general_parameters.jpg]]
+#+name: tab:meas_parameters
+#+caption: Impact test parameters
+| Start Delay | -5% |
+| Number of lines | 801 lines |
+| Trigger Threshold | 300N |
+| Trigger Hysteresis | 100mN |
+| FRF Average | 10 |
-Windowing is used on the force response signals.
+** Windowing
+Windowing is used on the force and response signals.
-A boxcar window (figure [[fig:window_force]]) is used for the force signal as once the impact on the structure is done, the measured signal is meaningless.
+A boxcar window (figure [[fig:windowing_force_signal]]) is used for the force signal as once the impact on the structure is done, the measured signal is meaningless.
+The parameters are:
+- *Start*: $3\%$
+- *Stop*: $7\%$
-An exponential window (figure [[fig:window_response]]) is used for the response signal as we are measuring transient signals and most of the information is located at the beginning of the signal.
-
-#+name: fig:window_force
-#+caption: Window used for the force signal
-#+attr_html: :width 500px
-[[file:img/parameters/window_force.jpg]]
-
-#+name: fig:window_response
-#+caption: Window used for the response signal
-#+attr_html: :width 500px
-[[file:img/parameters/window_response.jpg]]
-
-* Frequency Response Functions and Coherence Results
-** Matlab Init :noexport:ignore:
-#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
- <>
+#+begin_src matlab :exports none
+ figure;
+ plot(100*[0, 0.03, 0.03, 0.07, 0.07, 1], [0, 0, 1, 1, 0, 0]);
+ xlabel('Time [%]'); ylabel('Amplitude');
+ xlim([0, 100]); ylim([0, 1]);
#+end_src
-#+begin_src matlab :exports none :results silent :noweb yes
- <>
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/windowing_force_signal.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+ <>
#+end_src
-** Load Data
+#+NAME: fig:windowing_force_signal
+#+CAPTION: Window used for the force signal
+[[file:figs/windowing_force_signal.png]]
+
+An exponential window (figure [[fig:windowing_response_signal]]) is used for the response signal as we are measuring transient signals and most of the information is located at the beginning of the signal.
+The parameters are:
+- FlatTop:
+ - *Start*: $3\%$
+ - *Stop*: $2.96\%$
+- Decreasing point:
+ - *X*: $60.4\%$
+ - *Y*: $14.7\%$
+
+#+begin_src matlab :exports none
+ x0 = 0.296;
+ xd = 0.604;
+ yd = 0.147;
+
+ alpha = log(yd)/(x0 - xd);
+
+ t = x0:0.01:1.01;
+ y = exp(-alpha*(t-x0));
+
+ figure;
+ plot(100*[0, 0.03, 0.03, x0, t], [0, 0, 1, 1, y]);
+ xlabel('Time [%]'); ylabel('Amplitude');
+ xlim([0, 100]); ylim([0, 1]);
+#+end_src
+
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/windowing_response_signal.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+ <>
+#+end_src
+
+#+NAME: fig:windowing_response_signal
+#+CAPTION: Window used for the response signals
+[[file:figs/windowing_response_signal.png]]
+
+* Force and Response signals
+Let's load some obtained data to look at the force and response signals.
+
#+begin_src matlab
- meas1_raw = load('modal_analysis/raw_data/Measurement1.mat');
+ meas1_raw = load('mat/meas_raw_1.mat');
#+end_src
** Raw Force Data
+The force input for the first measurement is shown on figure [[fig:raw_data_force]]. We can see 10 impacts, one zoom on one impact is shown on figure [[fig:raw_data_force_zoom]].
+
+The Fourier transform of the force is shown on figure [[fig:fourier_transfor_force_impact]]. This has been obtained without any windowing.
+
#+begin_src matlab :exports none
time = linspace(0, meas1_raw.Track1_X_Resolution*length(meas1_raw.Track1), length(meas1_raw.Track1));
+#+end_src
+
+#+begin_src matlab :exports none
figure;
plot(time, meas1_raw.Track1);
xlabel('Time [s]');
@@ -266,6 +347,10 @@ An exponential window (figure [[fig:window_response]]) is used for the response
[[file:figs/raw_data_force.png]]
#+begin_src matlab :exports none
+ figure;
+ plot(time, meas1_raw.Track1);
+ xlabel('Time [s]');
+ ylabel('Force [N]');
xlim([22.1, 22.3]);
#+end_src
@@ -278,7 +363,54 @@ An exponential window (figure [[fig:window_response]]) is used for the response
#+CAPTION: Raw Force Data from Hammer Blow - Zoom
[[file:figs/raw_data_force_zoom.png]]
+#+begin_src matlab :exports none
+ Fs = 1/meas1_raw.Track1_X_Resolution; % Sampling Frequency [Hz]
+ impacts = [5.9, 11.2, 16.6, 22.2, 27.3, 32.7, 38.1, 43.8, 50.4]; % Time just before the impact occurs [s]
+
+ L = 8194;
+ f = Fs*(0:(L/2))/L; % Frequency vector [Hz]
+
+ F_fft = zeros((8193+1)/2+1, length(impacts));
+
+ for i = 1:length(impacts)
+ t0 = impacts(i);
+ [~, i_start] = min(abs(time-t0));
+ i_end = i_start + 8193;
+
+ Y = fft(meas1_raw.Track1(i_start:i_end));
+
+ P2 = abs(Y/L);
+ P1 = P2(1:L/2+1);
+ P1(2:end-1) = 2*P1(2:end-1);
+ F_fft(:, i) = P1;
+ end
+#+end_src
+
+#+begin_src matlab :exports none
+ figure;
+ hold on;
+ for i = 1:length(impacts)
+ plot(f, F_fft(:, i), '-k');
+ end
+ hold off;
+ xlim([0, 200]);
+ xlabel('Frequency [Hz]'); ylabel('Force [N]');
+#+end_src
+
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/fourier_transfor_force_impact.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+ <>
+#+end_src
+
+#+NAME: fig:fourier_transfor_force_impact
+#+CAPTION: Fourier Transform of the 10 force impacts for the first measurement
+[[file:figs/fourier_transfor_force_impact.png]]
+
** Raw Response Data
+The response signal for the first measurement is shown on figure [[fig:raw_data_acceleration]]. One zoom on one response is shown on figure [[fig:raw_data_acceleration_zoom]].
+
+The Fourier transform of the response signals is shown on figure [[fig:fourier_transform_response_signals]]. This has been obtained without any windowing.
+
#+begin_src matlab :exports none
figure;
plot(time, meas1_raw.Track2);
@@ -296,6 +428,10 @@ An exponential window (figure [[fig:window_response]]) is used for the response
[[file:figs/raw_data_acceleration.png]]
#+begin_src matlab :exports none
+ figure;
+ plot(time, meas1_raw.Track2);
+ xlabel('Time [s]');
+ ylabel('Acceleration [m/s2]');
xlim([22.1, 22.5]);
#+end_src
@@ -308,16 +444,96 @@ An exponential window (figure [[fig:window_response]]) is used for the response
#+CAPTION: Raw Acceleration Data from Accelerometer - Zoom
[[file:figs/raw_data_acceleration_zoom.png]]
-** Load Data
-#+begin_src matlab
- meas1 = load('modal_analysis/frf_coh/Measurement1.mat');
+#+begin_src matlab :exports none
+ X_fft = zeros((8193+1)/2+1, length(impacts));
+
+ for i = 1:length(impacts)
+ t0 = impacts(i);
+ [~, i_start] = min(abs(time-t0));
+ i_end = i_start + 8193;
+
+ Y = fft(meas1_raw.Track2(i_start:i_end));
+
+ P2 = abs(Y/L);
+ P1 = P2(1:L/2+1);
+ P1(2:end-1) = 2*P1(2:end-1);
+ X_fft(:, i) = P1;
+ end
#+end_src
-** FRF and Coherence Results
+#+begin_src matlab :exports none
+ figure;
+ hold on;
+ for i = 1:length(impacts)
+ plot(f, X_fft(:, i), '-k');
+ end
+ hold off;
+ xlim([0, 200]);
+ set(gca, 'Yscale', 'log');
+ xlabel('Frequency [Hz]'); ylabel('Acceleration [$m/s^2$]');
+#+end_src
+
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/fourier_transform_response_signals.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+ <>
+#+end_src
+
+#+NAME: fig:fourier_transform_response_signals
+#+CAPTION: Fourier transform of the measured response signals
+[[file:figs/fourier_transform_response_signals.png]]
+
+** Computation of one Frequency Response Function
+Now that we have obtained the Fourier transform of both the force input and the response signal, we can compute the Frequency Response Function from the force to the acceleration.
+
+We then compare the result obtained with the FRF computed by the modal software (figure [[fig:frf_comparison_software]]).
+
+The slight difference can probably be explained by the use of windows.
+
+In the following analysis, FRF computed from the software will be used.
+
+#+begin_src matlab
+ meas1 = load('mat/meas_frf_coh_1.mat');
+#+end_src
+
+#+begin_src matlab :exports none
+ figure;
+ hold on;
+ for i = 1:length(impacts)
+ plot(f, X_fft(:, i)./F_fft(:, i), '-k');
+ end
+ plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvSpc_2_RMS_Y_Val)
+ hold off;
+ xlim([0, 200]);
+ set(gca, 'Yscale', 'log');
+ xlabel('Frequency [Hz]'); ylabel('Acceleration/Force [$m/s^2/N$]');
+#+end_src
+
+#+HEADER: :tangle no :exports results :results none :noweb yes
+#+begin_src matlab :var filepath="figs/frf_comparison_software.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+ <>
+#+end_src
+
+#+NAME: fig:frf_comparison_software
+#+CAPTION: Comparison of the computed FRF from the Fourier transform and using the modal software
+[[file:figs/frf_comparison_software.png]]
+
+* Frequency Response Functions and Coherence Results
+Let's see one computed Frequency Response Function and one coherence in order to attest the quality of the measurement.
+
+First, we load the data.
+#+begin_src matlab
+ meas1 = load('mat/meas_frf_coh_1.mat');
+#+end_src
+
+And we plot on figure [[fig:frf_result_example]] the frequency response function from the force applied in the $X$ direction at the location of the accelerometer number 11 to the acceleration in the $X$ direction as measured by the first accelerometer located on the top platform of the hexapod.
+
+The coherence associated is shown on figure [[fig:frf_result_example]].
+
#+begin_src matlab :exports none
figure;
ax1 = subplot(2, 1, 1);
plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvXSpc_2_1_RMS_Y_Mod);
+ set(gca, 'Yscale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude');
@@ -347,7 +563,7 @@ An exponential window (figure [[fig:window_response]]) is used for the response
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
-#+begin_src matlab :var filepath="figs/coh_result_example.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+#+begin_src matlab :var filepath="figs/coh_result_example.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
<>
#+end_src
@@ -355,1137 +571,81 @@ An exponential window (figure [[fig:window_response]]) is used for the response
#+CAPTION: Example of one measured Coherence
[[file:figs/coh_result_example.png]]
-* Mode Shapes
-Multiple modal extraction techniques can be used (SIMO, MIMO, narrow band, wide band, ...).
-First preliminary results on 10 identified modes are presented here.
+* Generation of a FRF matrix and a Coherence matrix from the measurements
+We want here to combine all the Frequency Response Functions measured into one big array called the *Frequency Response Matrix*.
-#+name: fig:mode1
-#+caption: Mode 1
-[[file:img/modes/mode1.gif]]
+The frequency response matrix is an $n \times p \times q$:
+- $n$ is the number of measurements: $23 \times 3$ (23 accelerometers measuring 3 directions each)
+- $p$ is the number of excitation inputs: $3$
+- $q$ is the number of frequency points $\omega_i$
-#+name: fig:mode2
-#+caption: Mode 2
-[[file:img/modes/mode2.gif]]
-
-#+name: fig:mode3
-#+caption: Mode 3
-[[file:img/modes/mode3.gif]]
-
-#+name: fig:mode4
-#+caption: Mode 4
-[[file:img/modes/mode4.gif]]
-
-#+name: fig:mode5
-#+caption: Mode 5
-[[file:img/modes/mode5.gif]]
-
-#+name: fig:mode6
-#+caption: Mode 6
-[[file:img/modes/mode6.gif]]
-
-#+name: fig:mode7
-#+caption: Mode 7
-[[file:img/modes/mode7.gif]]
-
-#+name: fig:mode8
-#+caption: Mode 8
-[[file:img/modes/mode8.gif]]
-
-#+name: fig:mode9
-#+caption: Mode 9
-[[file:img/modes/mode9.gif]]
-
-#+name: fig:mode10
-#+caption: Mode 10
-[[file:img/modes/mode10.gif]]
-
-* Obtained Modal Matrices
-From the modal analysis software, we can export the obtained *eigen matrices*:
-\[ \begin{bmatrix}
- \omega_1^2 & & 0 \\
- & \ddots & \\
- 0 & & \omega_n^2
-\end{bmatrix}; \quad \Psi = \begin{bmatrix}
- & & \\
- \{\psi_1\} & \dots & \{\psi_n\} \\
- & &
-\end{bmatrix} \]
-
-where $\bar{\omega}_r^2$ is the $r^\text{th}$ eigenvalue squared and $\{\phi\}_r$ is a description of the corresponding *mode shape*.
-
-The file containing the eigen frequencies and mode shapes are shown below (for the first mode).
-
-#+begin_src bash :results output :exports results :eval no-export
- sed 80q modal_analysis/modes_propres_narband.asc
-#+end_src
-
-#+RESULTS:
-#+begin_example
-Created by N-Modal
-Estimator: cmif
-18-Jun-19 16:31:25
+Thus, the FRF matrix is an $69 \times 3 \times 801$ matrix.
-Mode 1
-freq = 11.11191Hz
-damp = 10.51401%
-modal A = 8.52879e+003-2.29043e+003i
-modal B = -9.64203e+004-6.08978e+005i
-Mode matrix of local coordinate [DOF: Re IM]
- 1X+: -9.34637e-002 4.52445e-002
- 1Y+: 2.33790e-001 1.41439e-003
- 1Z+: -1.73754e-002 6.02449e-003
- 2X+: -7.42108e-002 3.91543e-002
- 2Y+: 2.41566e-001 -1.44869e-003
- 2Z+: -5.99285e-003 2.10370e-003
- 4X+: -1.02163e-001 2.79561e-002
- 4Y+: 2.29048e-001 2.89782e-002
- 4Z+: -2.85130e-002 1.77132e-004
- 5X+: -8.77132e-002 3.34081e-002
- 5Y+: 2.14182e-001 2.14655e-002
- 5Z+: -1.54521e-002 1.26682e-002
- 6X+: -7.90143e-002 2.42583e-002
- 6Y+: 2.20669e-001 2.12738e-002
- 6Z+: 4.60755e-002 4.96406e-003
- 7X+: -7.79654e-002 2.58385e-002
- 7Y+: 2.06861e-001 3.48019e-002
- 7Z+: -1.78311e-002 -1.29704e-002
- 8X+: -8.49357e-002 3.55200e-002
- 8Y+: 2.07470e-001 3.59745e-002
- 8Z+: -7.66974e-002 -3.19813e-003
- 9X+: -7.38565e-002 1.95146e-002
- 9Y+: 2.17403e-001 2.01550e-002
- 9Z+: -1.77073e-002 -3.46414e-003
- 10X+: -7.77587e-002 2.36700e-002
- 10Y+: 2.35654e-001 -2.14540e-002
- 10Z+: 7.94165e-002 -2.45897e-002
- 11X+: -8.17972e-002 2.20583e-002
- 11Y+: 2.20906e-001 -4.30164e-003
- 11Z+: -5.60520e-003 3.10187e-003
- 12X+: -8.64261e-002 3.66022e-002
- 12Y+: 2.15000e-001 -5.74661e-003
- 12Z+: -1.22622e-001 4.11767e-002
- 13X+: -4.25169e-002 1.56602e-002
- 13Y+: 5.31036e-002 -1.73951e-002
- 13Z+: -4.07130e-002 1.26884e-002
- 14X+: -3.85032e-002 1.29431e-002
- 14Y+: 5.36716e-002 -1.80868e-002
- 14Z+: 1.00367e-001 -3.48798e-002
- 15X+: -4.25524e-002 1.46363e-002
- 15Y+: 5.19668e-002 -1.69744e-002
- 15Z+: 5.89747e-003 -2.32428e-003
- 16X+: -4.31268e-002 1.38332e-002
- 16Y+: 5.07545e-002 -1.53045e-002
- 16Z+: -1.04172e-001 3.17984e-002
- 17X+: -2.69757e-002 9.07955e-003
- 17Y+: 3.07837e-002 -9.44663e-003
- 17Z+: -7.63502e-003 1.68203e-003
- 18X+: -3.00097e-002 9.23966e-003
- 18Y+: 2.83585e-002 -8.97747e-003
- 18Z+: 1.52467e-001 -4.78675e-002
- 19X+: -2.70223e-002 6.16478e-003
- 19Y+: 3.06149e-002 -6.25382e-003
- 19Z+: -4.84888e-003 1.93970e-003
- 20X+: -2.90976e-002 7.13184e-003
- 20Y+: 3.36738e-002 -7.30875e-003
- 20Z+: -1.66902e-001 3.93419e-002
- 3X+: -9.40720e-002 3.93724e-002
- 3Y+: 2.52307e-001 0.00000e+000
- 3Z+: -1.53864e-002 -9.25720e-004
- 21X+: -7.91940e-002 4.39648e-002
- 21Y+: 2.04567e-001 9.49987e-003
- 21Z+: -1.56087e-002 7.08838e-003
- 22X+: -1.01070e-001 3.13534e-002
- 22Y+: 1.92270e-001 1.80423e-002
- 22Z+: 2.93053e-003 -1.97308e-003
- 23X+: -8.86455e-002 4.29906e-002
- 23Z+: -3.38351e-002 1.81362e-003
- 23Y-: -1.90862e-001 -2.53414e-002
-#+end_example
+#+begin_important
+For each frequency point $\omega_i$, we obtain a 2D matrix:
+\begin{equation}
+ \text{FRF}(\omega_i) = \begin{bmatrix}
+ \frac{D_{1_x}}{F_x}(\omega_i) & \frac{D_{1_x}}{F_y}(\omega_i) & \frac{D_{1_x}}{F_z}(\omega_i) \\
+ \frac{D_{1_y}}{F_x}(\omega_i) & \frac{D_{1_y}}{F_y}(\omega_i) & \frac{D_{1_y}}{F_z}(\omega_i) \\
+ \frac{D_{1_z}}{F_x}(\omega_i) & \frac{D_{1_z}}{F_y}(\omega_i) & \frac{D_{1_z}}{F_z}(\omega_i) \\
+ \frac{D_{2_x}}{F_x}(\omega_i) & \frac{D_{2_x}}{F_y}(\omega_i) & \frac{D_{2_x}}{F_z}(\omega_i) \\
+ \vdots & \vdots & \vdots \\
+ \frac{D_{23_z}}{F_x}(\omega_i) & \frac{D_{23_z}}{F_y}(\omega_i) & \frac{D_{23_z}}{F_z}(\omega_i) \\
+\end{bmatrix}
+\end{equation}
+#+end_important
-* Compute the Modal Model
-** Matlab Init :noexport:ignore:
-#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
- <>
-#+end_src
-
-#+begin_src matlab :exports none :results silent :noweb yes
- <>
-#+end_src
-
-** Position of the accelerometers
-There are 23 accelerometers:
-- 4 on the bottom granite
-- 4 on the top granite
-- 4 on top of the translation stage
-- 4 on the tilt stage
-- 3 on top of the spindle
-- 4 on top of the hexapod
-
-The coordinates defined in the software are displayed below.
-
-#+begin_src bash :results output :exports results :eval no-export
- sed -n 18,40p modal_analysis/acc_coordinates.txt | tac --
-#+end_src
-
-#+RESULTS:
-#+begin_example
- 1 1.0000e-001 1.0000e-001 1.1500e+000 0 Top
- 2 1.0000e-001 -1.0000e-001 1.1500e+000 0 Top
- 3 -1.0000e-001 -1.0000e-001 1.1500e+000 0 Top
- 4 -1.0000e-001 1.0000e-001 1.1500e+000 0 Top
- 5 4.0000e-001 4.0000e-001 9.5000e-001 0 inner
- 6 4.0000e-001 -4.0000e-001 9.5000e-001 0 inner
- 7 -4.0000e-001 -4.0000e-001 9.5000e-001 0 inner
- 8 -4.0000e-001 4.0000e-001 9.5000e-001 0 inner
- 9 5.0000e-001 5.0000e-001 9.0000e-001 0 outer
- 10 5.0000e-001 -5.0000e-001 9.0000e-001 0 outer
- 11 -5.0000e-001 -5.0000e-001 9.0000e-001 0 outer
- 12 -5.0000e-001 5.0000e-001 9.0000e-001 0 outer
- 13 5.5000e-001 5.5000e-001 5.5000e-001 0 top
- 14 5.5000e-001 -5.5000e-001 5.5000e-001 0 top
- 15 -5.5000e-001 -5.5000e-001 5.5000e-001 0 top
- 16 -5.5000e-001 5.5000e-001 5.5000e-001 0 top
- 17 9.5000e-001 9.5000e-001 4.0000e-001 0 low
- 18 9.5000e-001 -9.5000e-001 4.0000e-001 0 low
- 19 -9.5000e-001 -9.5000e-001 4.0000e-001 0 low
- 20 -9.5000e-001 9.5000e-001 4.0000e-001 0 low
- 21 2.0000e-001 2.0000e-001 8.5000e-001 0 bot
- 22 0.0000e+000 -2.0000e-001 8.5000e-001 0 bot
- 23 -2.0000e-001 2.0000e-001 8.5000e-001 0 bot
-#+end_example
-
-#+name: tab:acc_location
-#+caption: Location of each Accelerometer (using the normal coordinate frame with X aligned with the X ray)
-| *Node number* | *Solid Body* | *Location* | *X* | *Y* | *Z* |
-|---------------+-------------------+------------+-------+-------+------|
-| 1 | Hexapod - Top | -X/-Y | -0.10 | -0.10 | 1.15 |
-| 2 | | -X/+Y | -0.10 | 0.10 | 1.15 |
-| 3 | | +X/+Y | 0.10 | 0.10 | 1.15 |
-| 4 | | +X/-Y | 0.10 | -0.10 | 1.15 |
-|---------------+-------------------+------------+-------+-------+------|
-| 5 | Tilt - Top | -X/-Y | -0.40 | -0.40 | 0.95 |
-| 6 | | -X/+Y | -0.40 | 0.40 | 0.95 |
-| 7 | | +X/+Y | 0.40 | 0.40 | 0.95 |
-| 8 | | +X/-Y | 0.40 | -0.40 | 0.95 |
-|---------------+-------------------+------------+-------+-------+------|
-| 9 | Translation - Top | -X/-Y | -0.50 | -0.50 | 0.90 |
-| 10 | | -X/+Y | -0.50 | 0.50 | 0.90 |
-| 11 | | +X/+Y | 0.50 | 0.50 | 0.90 |
-| 12 | | +X/-Y | 0.50 | -0.50 | 0.90 |
-|---------------+-------------------+------------+-------+-------+------|
-| 13 | Top Granite | -X/-Y | -0.55 | -0.50 | 0.55 |
-| 14 | | -X/+Y | -0.55 | 0.50 | 0.55 |
-| 15 | | +X/+Y | 0.55 | 0.50 | 0.55 |
-| 16 | | +X/-Y | 0.55 | -0.50 | 0.55 |
-|---------------+-------------------+------------+-------+-------+------|
-| 17 | Bottom Granite | -X/-Y | -0.95 | -0.90 | 0.40 |
-| 18 | | -X/+Y | -0.95 | 0.90 | 0.40 |
-| 19 | | +X/+Y | 0.95 | 0.90 | 0.40 |
-| 20 | | +X/-Y | 0.95 | -0.90 | 0.40 |
-|---------------+-------------------+------------+-------+-------+------|
-| 21 | Spindle - Top | -X/-Y | -0.20 | -0.20 | 0.85 |
-| 22 | | +0/+Y | 0.00 | 0.20 | 0.85 |
-| 23 | | +X/-Y | 0.20 | -0.20 | 0.85 |
-
-** Define positions of the accelerometers on matlab
-We define the X-Y-Z position of each sensor.
-Each line corresponds to one accelerometer, X-Y-Z position in meter.
+We generate such FRF matrix from the measurements using the following script.
#+begin_src matlab
- positions = [...
- -0.10, -0.10, 1.15 ; ...
- -0.10, 0.10, 1.15 ; ...
- 0.10, 0.10, 1.15 ; ...
- 0.10, -0.10, 1.15 ; ...
- -0.40, -0.40, 0.95 ; ...
- -0.40, 0.40, 0.95 ; ...
- 0.40, 0.40, 0.95 ; ...
- 0.40, -0.40, 0.95 ; ...
- -0.50, -0.50, 0.90 ; ...
- -0.50, 0.50, 0.90 ; ...
- 0.50, 0.50, 0.90 ; ...
- 0.50, -0.50, 0.90 ; ...
- -0.55, -0.50, 0.55 ; ...
- -0.55, 0.50, 0.55 ; ...
- 0.55, 0.50, 0.55 ; ...
- 0.55, -0.50, 0.55 ; ...
- -0.95, -0.90, 0.40 ; ...
- -0.95, 0.90, 0.40 ; ...
- 0.95, 0.90, 0.40 ; ...
- 0.95, -0.90, 0.40 ; ...
- -0.20, -0.20, 0.85 ; ...
- 0.00, 0.20, 0.85 ; ...
- 0.20, -0.20, 0.85 ];
-#+end_src
+ n_meas = 24;
+ n_acc = 23;
+ dirs = 'XYZ';
-#+begin_src matlab
- figure;
- hold on;
- fill3(positions(1:4, 1), positions(1:4, 2), positions(1:4, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(5:8, 1), positions(5:8, 2), positions(5:8, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(9:12, 1), positions(9:12, 2), positions(9:12, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(13:16, 1), positions(13:16, 2), positions(13:16, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(17:20, 1), positions(17:20, 2), positions(17:20, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(21:23, 1), positions(21:23, 2), positions(21:23, 3), 'k', 'FaceAlpha', 0.5)
- hold off;
-#+end_src
+ % Number of Accelerometer * DOF for each acccelerometer / Number of excitation / frequency points
+ FRFs = zeros(3*n_acc, 3, 801);
+ COHs = zeros(3*n_acc, 3, 801);
-** Import the modal vectors on matlab
-*** Mode1
-#+begin_src bash :results output :exports none :eval no-export
- sed -n 12,80p modal_analysis/modes_propres_narband.asc
-#+end_src
+ % Loop through measurements
+ for i = 1:n_meas
+ % Load the measurement file
+ meas = load(sprintf('mat/meas_frf_coh_%i.mat', i));
-#+RESULTS:
-#+begin_example
- 1X+: -9.34637e-002 4.52445e-002
- 1Y+: 2.33790e-001 1.41439e-003
- 1Z+: -1.73754e-002 6.02449e-003
- 2X+: -7.42108e-002 3.91543e-002
- 2Y+: 2.41566e-001 -1.44869e-003
- 2Z+: -5.99285e-003 2.10370e-003
- 4X+: -1.02163e-001 2.79561e-002
- 4Y+: 2.29048e-001 2.89782e-002
- 4Z+: -2.85130e-002 1.77132e-004
- 5X+: -8.77132e-002 3.34081e-002
- 5Y+: 2.14182e-001 2.14655e-002
- 5Z+: -1.54521e-002 1.26682e-002
- 6X+: -7.90143e-002 2.42583e-002
- 6Y+: 2.20669e-001 2.12738e-002
- 6Z+: 4.60755e-002 4.96406e-003
- 7X+: -7.79654e-002 2.58385e-002
- 7Y+: 2.06861e-001 3.48019e-002
- 7Z+: -1.78311e-002 -1.29704e-002
- 8X+: -8.49357e-002 3.55200e-002
- 8Y+: 2.07470e-001 3.59745e-002
- 8Z+: -7.66974e-002 -3.19813e-003
- 9X+: -7.38565e-002 1.95146e-002
- 9Y+: 2.17403e-001 2.01550e-002
- 9Z+: -1.77073e-002 -3.46414e-003
- 10X+: -7.77587e-002 2.36700e-002
- 10Y+: 2.35654e-001 -2.14540e-002
- 10Z+: 7.94165e-002 -2.45897e-002
- 11X+: -8.17972e-002 2.20583e-002
- 11Y+: 2.20906e-001 -4.30164e-003
- 11Z+: -5.60520e-003 3.10187e-003
- 12X+: -8.64261e-002 3.66022e-002
- 12Y+: 2.15000e-001 -5.74661e-003
- 12Z+: -1.22622e-001 4.11767e-002
- 13X+: -4.25169e-002 1.56602e-002
- 13Y+: 5.31036e-002 -1.73951e-002
- 13Z+: -4.07130e-002 1.26884e-002
- 14X+: -3.85032e-002 1.29431e-002
- 14Y+: 5.36716e-002 -1.80868e-002
- 14Z+: 1.00367e-001 -3.48798e-002
- 15X+: -4.25524e-002 1.46363e-002
- 15Y+: 5.19668e-002 -1.69744e-002
- 15Z+: 5.89747e-003 -2.32428e-003
- 16X+: -4.31268e-002 1.38332e-002
- 16Y+: 5.07545e-002 -1.53045e-002
- 16Z+: -1.04172e-001 3.17984e-002
- 17X+: -2.69757e-002 9.07955e-003
- 17Y+: 3.07837e-002 -9.44663e-003
- 17Z+: -7.63502e-003 1.68203e-003
- 18X+: -3.00097e-002 9.23966e-003
- 18Y+: 2.83585e-002 -8.97747e-003
- 18Z+: 1.52467e-001 -4.78675e-002
- 19X+: -2.70223e-002 6.16478e-003
- 19Y+: 3.06149e-002 -6.25382e-003
- 19Z+: -4.84888e-003 1.93970e-003
- 20X+: -2.90976e-002 7.13184e-003
- 20Y+: 3.36738e-002 -7.30875e-003
- 20Z+: -1.66902e-001 3.93419e-002
- 3X+: -9.40720e-002 3.93724e-002
- 3Y+: 2.52307e-001 0.00000e+000
- 3Z+: -1.53864e-002 -9.25720e-004
- 21X+: -7.91940e-002 4.39648e-002
- 21Y+: 2.04567e-001 9.49987e-003
- 21Z+: -1.56087e-002 7.08838e-003
- 22X+: -1.01070e-001 3.13534e-002
- 22Y+: 1.92270e-001 1.80423e-002
- 22Z+: 2.93053e-003 -1.97308e-003
- 23X+: -8.86455e-002 4.29906e-002
- 23Z+: -3.38351e-002 1.81362e-003
- 23Y-: -1.90862e-001 -2.53414e-002
-#+end_example
+ % First: determine what is the exitation (direction and sign)
+ exc_dir = meas.FFT1_AvXSpc_2_1_RMS_RfName(end);
+ exc_sign = meas.FFT1_AvXSpc_2_1_RMS_RfName(end-1);
+ % Determine what is the correct excitation sign
+ exc_factor = str2num([exc_sign, '1']);
+ if exc_dir ~= 'Z'
+ exc_factor = exc_factor*(-1);
+ end
-#+begin_src matlab
- mode1 = [...
- -9.34637e-002+j*4.52445e-002, +2.33790e-001+j*1.41439e-003, -1.73754e-002+j*6.02449e-003;
- -7.42108e-002+j*3.91543e-002, +2.41566e-001-j*1.44869e-003, -5.99285e-003+j*2.10370e-003;
- -9.40720e-002+j*3.93724e-002, +2.52307e-001+j*0.00000e+000, -1.53864e-002-j*9.25720e-004;
- -1.02163e-001+j*2.79561e-002, +2.29048e-001+j*2.89782e-002, -2.85130e-002+j*1.77132e-004;
- -8.77132e-002+j*3.34081e-002, +2.14182e-001+j*2.14655e-002, -1.54521e-002+j*1.26682e-002;
- -7.90143e-002+j*2.42583e-002, +2.20669e-001+j*2.12738e-002, +4.60755e-002+j*4.96406e-003;
- -7.79654e-002+j*2.58385e-002, +2.06861e-001+j*3.48019e-002, -1.78311e-002-j*1.29704e-002;
- -8.49357e-002+j*3.55200e-002, +2.07470e-001+j*3.59745e-002, -7.66974e-002-j*3.19813e-003;
- -7.38565e-002+j*1.95146e-002, +2.17403e-001+j*2.01550e-002, -1.77073e-002-j*3.46414e-003;
- -7.77587e-002+j*2.36700e-002, +2.35654e-001-j*2.14540e-002, +7.94165e-002-j*2.45897e-002;
- -8.17972e-002+j*2.20583e-002, +2.20906e-001-j*4.30164e-003, -5.60520e-003+j*3.10187e-003;
- -8.64261e-002+j*3.66022e-002, +2.15000e-001-j*5.74661e-003, -1.22622e-001+j*4.11767e-002;
- -4.25169e-002+j*1.56602e-002, +5.31036e-002-j*1.73951e-002, -4.07130e-002+j*1.26884e-002;
- -3.85032e-002+j*1.29431e-002, +5.36716e-002-j*1.80868e-002, +1.00367e-001-j*3.48798e-002;
- -4.25524e-002+j*1.46363e-002, +5.19668e-002-j*1.69744e-002, +5.89747e-003-j*2.32428e-003;
- -4.31268e-002+j*1.38332e-002, +5.07545e-002-j*1.53045e-002, -1.04172e-001+j*3.17984e-002;
- -2.69757e-002+j*9.07955e-003, +3.07837e-002-j*9.44663e-003, -7.63502e-003+j*1.68203e-003;
- -3.00097e-002+j*9.23966e-003, +2.83585e-002-j*8.97747e-003, +1.52467e-001-j*4.78675e-002;
- -2.70223e-002+j*6.16478e-003, +3.06149e-002-j*6.25382e-003, -4.84888e-003+j*1.93970e-003;
- -2.90976e-002+j*7.13184e-003, +3.36738e-002-j*7.30875e-003, -1.66902e-001+j*3.93419e-002;
- -7.91940e-002+j*4.39648e-002, +2.04567e-001+j*9.49987e-003, -1.56087e-002+j*7.08838e-003;
- -1.01070e-001+j*3.13534e-002, +1.92270e-001+j*1.80423e-002, +2.93053e-003-j*1.97308e-003;
- -8.86455e-002+j*4.29906e-002, +1.90862e-001+j*2.53414e-002, -3.38351e-002+j*1.81362e-003];
-#+end_src
+ % Then: loop through the nine measurements and store them at the correct location
+ for j = 2:10
+ % Determine what is the accelerometer and direction
+ [indices_acc_i] = strfind(meas.(sprintf('FFT1_H1_%i_1_RpName', j)), '.');
+ acc_i = str2num(meas.(sprintf('FFT1_H1_%i_1_RpName', j))(indices_acc_i(1)+1:indices_acc_i(2)-1));
-*** Mode2
-#+begin_src bash :results output :exports none :eval no-export
- sed -n 88,156p modal_analysis/modes_propres_narband.asc
-#+end_src
-
-#+RESULTS:
-#+begin_example
- 1X+: 7.56931e-002 3.61548e-002
- 1Y+: 2.07574e-001 1.69205e-004
- 1Z+: 1.29733e-002 -6.78426e-004
- 2X+: 8.58732e-002 2.54470e-002
- 2Y+: 2.07117e-001 -1.31755e-003
- 2Z+: -2.13788e-003 -1.24974e-002
- 4X+: 7.09825e-002 3.66313e-002
- 4Y+: 2.09969e-001 1.11484e-002
- 4Z+: 9.19478e-003 3.47272e-002
- 5X+: 6.23935e-002 1.02488e-002
- 5Y+: 2.30687e-001 -3.58416e-003
- 5Z+: 3.27122e-002 -5.85468e-002
- 6X+: 7.61163e-002 -2.43630e-002
- 6Y+: 2.26743e-001 -1.15334e-002
- 6Z+: -6.20205e-003 -1.21742e-001
- 7X+: 8.01824e-002 -1.94769e-002
- 7Y+: 1.97485e-001 4.50105e-002
- 7Z+: -2.21170e-002 9.77052e-002
- 8X+: 6.19294e-002 8.15075e-003
- 8Y+: 2.03864e-001 4.45835e-002
- 8Z+: 2.55133e-002 1.36137e-001
- 9X+: 4.38135e-002 7.30537e-002
- 9Y+: 2.28426e-001 -6.58868e-003
- 9Z+: 1.16313e-002 5.09427e-004
- 10X+: 5.45770e-002 4.34251e-002
- 10Y+: 2.50823e-001 0.00000e+000
- 10Z+: -4.63460e-002 -4.76868e-002
- 11X+: 5.50987e-002 4.26178e-002
- 11Y+: 2.29394e-001 5.78236e-002
- 11Z+: 1.90158e-002 1.09139e-002
- 12X+: 4.98867e-002 7.30190e-002
- 12Y+: 2.07871e-001 4.57750e-002
- 12Z+: 6.69433e-002 9.00315e-002
- 13X+: 2.48819e-002 3.03222e-002
- 13Y+: -2.56046e-002 -3.34132e-002
- 13Z+: 2.13260e-002 2.58544e-002
- 14X+: 2.45706e-002 2.60221e-002
- 14Y+: -2.57723e-002 -3.35612e-002
- 14Z+: -5.71282e-002 -6.61562e-002
- 15X+: 2.68196e-002 2.83888e-002
- 15Y+: -2.57263e-002 -3.29627e-002
- 15Z+: -2.11722e-003 -3.37239e-003
- 16X+: 2.51442e-002 3.32558e-002
- 16Y+: -2.54372e-002 -3.25062e-002
- 16Z+: 5.65780e-002 7.64142e-002
- 17X+: 1.62437e-002 1.94534e-002
- 17Y+: -1.31293e-002 -2.05924e-002
- 17Z+: 1.05274e-003 3.59474e-003
- 18X+: 1.83431e-002 2.03836e-002
- 18Y+: -1.16818e-002 -1.86334e-002
- 18Z+: -8.66632e-002 -1.08216e-001
- 19X+: 1.62553e-002 1.79588e-002
- 19Y+: -1.28857e-002 -1.90512e-002
- 19Z+: 6.25653e-003 4.97733e-003
- 20X+: 1.63830e-002 2.03943e-002
- 20Y+: -1.48941e-002 -2.11717e-002
- 20Z+: 8.68045e-002 1.16491e-001
- 3X+: 8.17201e-002 2.36079e-002
- 3Y+: 2.15927e-001 1.61300e-002
- 3Z+: -5.48456e-004 2.55691e-002
- 21X+: 6.79204e-002 -5.55513e-002
- 21Y+: 2.32871e-001 2.33389e-002
- 21Z+: 1.34345e-002 -2.31815e-002
- 22X+: 4.02414e-002 -8.38957e-002
- 22Y+: 2.35273e-001 2.73256e-002
- 22Z+: -8.51632e-003 -7.49635e-003
- 23X+: 6.18293e-002 -5.99671e-002
- 23Z+: 1.63533e-002 6.09161e-002
- 23Y-: -2.37693e-001 -4.34204e-002
-#+end_example
-
-#+begin_src matlab
- mode2 = [...
- +7.56931e-002+j*3.61548e-002, +2.07574e-001+j*1.69205e-004, +1.29733e-002-j*6.78426e-004;
- +8.58732e-002+j*2.54470e-002, +2.07117e-001-j*1.31755e-003, -2.13788e-003-j*1.24974e-002;
- +8.17201e-002+j*2.36079e-002, +2.15927e-001+j*1.61300e-002, -5.48456e-004+j*2.55691e-002;
- +7.09825e-002+j*3.66313e-002, +2.09969e-001+j*1.11484e-002, +9.19478e-003+j*3.47272e-002;
- +6.23935e-002+j*1.02488e-002, +2.30687e-001-j*3.58416e-003, +3.27122e-002-j*5.85468e-002;
- +7.61163e-002-j*2.43630e-002, +2.26743e-001-j*1.15334e-002, -6.20205e-003-j*1.21742e-001;
- +8.01824e-002-j*1.94769e-002, +1.97485e-001+j*4.50105e-002, -2.21170e-002+j*9.77052e-002;
- +6.19294e-002+j*8.15075e-003, +2.03864e-001+j*4.45835e-002, +2.55133e-002+j*1.36137e-001;
- +4.38135e-002+j*7.30537e-002, +2.28426e-001-j*6.58868e-003, +1.16313e-002+j*5.09427e-004;
- +5.45770e-002+j*4.34251e-002, +2.50823e-001+j*0.00000e+000, -4.63460e-002-j*4.76868e-002;
- +5.50987e-002+j*4.26178e-002, +2.29394e-001+j*5.78236e-002, +1.90158e-002+j*1.09139e-002;
- +4.98867e-002+j*7.30190e-002, +2.07871e-001+j*4.57750e-002, +6.69433e-002+j*9.00315e-002;
- +2.48819e-002+j*3.03222e-002, -2.56046e-002-j*3.34132e-002, +2.13260e-002+j*2.58544e-002;
- +2.45706e-002+j*2.60221e-002, -2.57723e-002-j*3.35612e-002, -5.71282e-002-j*6.61562e-002;
- +2.68196e-002+j*2.83888e-002, -2.57263e-002-j*3.29627e-002, -2.11722e-003-j*3.37239e-003;
- +2.51442e-002+j*3.32558e-002, -2.54372e-002-j*3.25062e-002, +5.65780e-002+j*7.64142e-002;
- +1.62437e-002+j*1.94534e-002, -1.31293e-002-j*2.05924e-002, +1.05274e-003+j*3.59474e-003;
- +1.83431e-002+j*2.03836e-002, -1.16818e-002-j*1.86334e-002, -8.66632e-002-j*1.08216e-001;
- +1.62553e-002+j*1.79588e-002, -1.28857e-002-j*1.90512e-002, +6.25653e-003+j*4.97733e-003;
- +1.63830e-002+j*2.03943e-002, -1.48941e-002-j*2.11717e-002, +8.68045e-002+j*1.16491e-001;
- +6.79204e-002-j*5.55513e-002, +2.32871e-001+j*2.33389e-002, +1.34345e-002-j*2.31815e-002;
- +4.02414e-002-j*8.38957e-002, +2.35273e-001+j*2.73256e-002, -8.51632e-003-j*7.49635e-003;
- +6.18293e-002-j*5.99671e-002, +2.37693e-001+j*4.34204e-002, +1.63533e-002+j*6.09161e-002]
-#+end_src
-
-*** Mode3
-#+begin_src bash :results output :exports none :eval no-export
- sed -n 164,232p modal_analysis/modes_propres_narband.asc
-#+end_src
-
-#+RESULTS:
-#+begin_example
- 1X+: 1.34688e-001 -6.65071e-002
- 1Y+: 1.55316e-002 1.01277e-002
- 1Z+: -5.88466e-002 1.14294e-002
- 2X+: 1.53934e-001 -9.76990e-003
- 2Y+: 7.17487e-003 1.11925e-002
- 2Z+: -4.57205e-002 7.26573e-003
- 4X+: 1.37298e-001 -5.24661e-002
- 4Y+: 1.19427e-003 -5.39240e-002
- 4Z+: -1.25915e-002 5.38133e-003
- 5X+: 2.43192e-001 -3.17374e-002
- 5Y+: -2.15730e-001 -7.69941e-004
- 5Z+: -1.56268e-001 1.44118e-002
- 6X+: -7.27705e-002 -3.54943e-003
- 6Y+: -2.47706e-001 2.66480e-003
- 6Z+: -1.21590e-001 1.06054e-002
- 7X+: -7.25870e-002 -4.62024e-003
- 7Y+: 2.27073e-001 -3.69315e-002
- 7Z+: 1.22611e-001 -6.67337e-003
- 8X+: 2.32731e-001 -2.85516e-002
- 8Y+: 2.35389e-001 -3.81905e-002
- 8Z+: 5.35574e-002 4.30394e-004
- 9X+: 2.64170e-001 -2.67367e-002
- 9Y+: -2.56227e-001 3.97957e-005
- 9Z+: -1.95398e-001 2.23549e-002
- 10X+: -1.66953e-002 -7.95698e-003
- 10Y+: -2.66547e-001 -2.17687e-002
- 10Z+: 1.56278e-002 2.23786e-003
- 11X+: -3.42364e-002 -9.30205e-003
- 11Y+: 2.52340e-001 -7.47237e-003
- 11Z+: -9.51643e-004 3.64798e-003
- 12X+: 2.97574e-001 0.00000e+000
- 12Y+: 2.23170e-001 -1.37831e-002
- 12Z+: 1.06266e-001 2.30324e-003
- 13X+: 2.67178e-002 -4.15723e-004
- 13Y+: 6.75423e-003 -2.18428e-003
- 13Z+: -1.69423e-002 3.12395e-003
- 14X+: -1.12283e-002 2.86316e-004
- 14Y+: 5.08225e-003 -2.14053e-003
- 14Z+: 2.18339e-002 -3.25204e-003
- 15X+: -1.17948e-002 6.82873e-004
- 15Y+: 1.94914e-002 -2.42151e-003
- 15Z+: 2.68660e-003 -2.92104e-004
- 16X+: 1.19490e-002 1.72236e-005
- 16Y+: 1.83552e-002 -2.71289e-003
- 16Z+: -2.70914e-002 4.84164e-003
- 17X+: 1.00173e-002 -5.80552e-005
- 17Y+: -3.87262e-003 -1.19607e-003
- 17Z+: -8.53809e-003 1.48424e-003
- 18X+: -1.22262e-002 5.13096e-004
- 18Y+: -5.73905e-003 -1.07659e-003
- 18Z+: 3.51730e-002 -6.13814e-003
- 19X+: -1.43735e-002 -4.78552e-004
- 19Y+: 2.31135e-002 -6.30554e-004
- 19Z+: 1.80171e-003 -1.98835e-004
- 20X+: 9.17792e-003 5.36661e-004
- 20Y+: 2.18969e-002 -5.81759e-004
- 20Z+: -3.72117e-002 5.35813e-003
- 3X+: 1.61551e-001 1.65478e-002
- 3Y+: -4.12527e-004 -5.60909e-002
- 3Z+: -9.00640e-003 3.50754e-003
- 21X+: 3.38754e-002 -3.38703e-002
- 21Y+: -2.20843e-002 2.78581e-002
- 21Z+: -8.79541e-002 -3.67473e-003
- 22X+: 3.93064e-002 4.69476e-002
- 22Y+: -1.69132e-002 -1.04606e-002
- 22Z+: -1.85351e-002 1.33750e-003
- 23X+: 3.60396e-002 -2.46238e-002
- 23Z+: 3.57722e-003 3.64827e-003
- 23Y-: 1.92038e-002 6.65895e-002
-#+end_example
-
-#+begin_src matlab
- mode3 = [...
- +1.34688e-001-j*6.65071e-002, +1.55316e-002+j*1.01277e-002, -5.88466e-002+j*1.14294e-002;
- +1.53934e-001-j*9.76990e-003, +7.17487e-003+j*1.11925e-002, -4.57205e-002+j*7.26573e-003;
- +1.61551e-001+j*1.65478e-002, -4.12527e-004-j*5.60909e-002, -9.00640e-003+j*3.50754e-003;
- +1.37298e-001-j*5.24661e-002, +1.19427e-003-j*5.39240e-002, -1.25915e-002+j*5.38133e-003;
- +2.43192e-001-j*3.17374e-002, -2.15730e-001-j*7.69941e-004, -1.56268e-001+j*1.44118e-002;
- -7.27705e-002-j*3.54943e-003, -2.47706e-001+j*2.66480e-003, -1.21590e-001+j*1.06054e-002;
- -7.25870e-002-j*4.62024e-003, +2.27073e-001-j*3.69315e-002, +1.22611e-001-j*6.67337e-003;
- +2.32731e-001-j*2.85516e-002, +2.35389e-001-j*3.81905e-002, +5.35574e-002+j*4.30394e-004;
- +2.64170e-001-j*2.67367e-002, -2.56227e-001+j*3.97957e-005, -1.95398e-001+j*2.23549e-002;
- -1.66953e-002-j*7.95698e-003, -2.66547e-001-j*2.17687e-002, +1.56278e-002+j*2.23786e-003;
- -3.42364e-002-j*9.30205e-003, +2.52340e-001-j*7.47237e-003, -9.51643e-004+j*3.64798e-003;
- +2.97574e-001+j*0.00000e+000, +2.23170e-001-j*1.37831e-002, +1.06266e-001+j*2.30324e-003;
- +2.67178e-002-j*4.15723e-004, +6.75423e-003-j*2.18428e-003, -1.69423e-002+j*3.12395e-003;
- -1.12283e-002+j*2.86316e-004, +5.08225e-003-j*2.14053e-003, +2.18339e-002-j*3.25204e-003;
- -1.17948e-002+j*6.82873e-004, +1.94914e-002-j*2.42151e-003, +2.68660e-003-j*2.92104e-004;
- +1.19490e-002+j*1.72236e-005, +1.83552e-002-j*2.71289e-003, -2.70914e-002+j*4.84164e-003;
- +1.00173e-002-j*5.80552e-005, -3.87262e-003-j*1.19607e-003, -8.53809e-003+j*1.48424e-003;
- -1.22262e-002+j*5.13096e-004, -5.73905e-003-j*1.07659e-003, +3.51730e-002-j*6.13814e-003;
- -1.43735e-002-j*4.78552e-004, +2.31135e-002-j*6.30554e-004, +1.80171e-003-j*1.98835e-004;
- +9.17792e-003+j*5.36661e-004, +2.18969e-002-j*5.81759e-004, -3.72117e-002+j*5.35813e-003;
- +3.38754e-002-j*3.38703e-002, -2.20843e-002+j*2.78581e-002, -8.79541e-002-j*3.67473e-003;
- +3.93064e-002+j*4.69476e-002, -1.69132e-002-j*1.04606e-002, -1.85351e-002+j*1.33750e-003;
- +3.60396e-002-j*2.46238e-002, -1.92038e-002-j*6.65895e-002, +3.57722e-003+j*3.64827e-003];
-#+end_src
-
-*** Mode4
-#+begin_src bash :results output :exports none :eval no-export
- sed -n 240,308p modal_analysis/modes_propres_narband.asc
-#+end_src
-
-#+RESULTS:
-#+begin_example
- 1X+: -1.02501e-001 -1.43802e-001
- 1Y+: -1.07971e-001 5.61418e-004
- 1Z+: 1.87145e-001 -1.03605e-001
- 2X+: -9.44764e-002 -1.36856e-001
- 2Y+: -1.04428e-001 5.27790e-003
- 2Z+: 1.60710e-001 -7.74212e-002
- 4X+: -9.17242e-002 -1.36656e-001
- 4Y+: -1.34249e-001 -1.03884e-002
- 4Z+: 1.92123e-001 -1.25627e-001
- 5X+: 1.05875e-002 -1.03886e-001
- 5Y+: -8.26338e-002 3.58498e-002
- 5Z+: 2.55819e-001 -6.94290e-003
- 6X+: -4.58970e-002 -1.33904e-002
- 6Y+: -9.41660e-002 4.99682e-002
- 6Z+: 1.28276e-001 4.59685e-002
- 7X+: -6.01521e-002 -1.30165e-002
- 7Y+: 2.56439e-003 -6.78141e-002
- 7Z+: 5.03428e-002 -1.59420e-001
- 8X+: -1.00895e-002 -8.80550e-002
- 8Y+: 1.26327e-002 -8.14444e-002
- 8Z+: 1.59506e-001 -2.05360e-001
- 9X+: -3.04658e-003 -1.57921e-001
- 9Y+: -8.23501e-002 4.82748e-002
- 9Z+: 1.69315e-001 1.22804e-002
- 10X+: -8.25875e-002 -7.31038e-002
- 10Y+: -1.08668e-001 3.56364e-002
- 10Z+: 8.28567e-002 -4.49596e-003
- 11X+: -1.06792e-001 -6.95394e-002
- 11Y+: 3.77195e-002 -7.65410e-002
- 11Z+: 8.00590e-003 -2.32461e-002
- 12X+: -4.84292e-002 -1.45790e-001
- 12Y+: 1.03862e-002 -7.31212e-002
- 12Z+: 1.78122e-001 -1.00939e-001
- 13X+: -3.49891e-002 -6.20969e-003
- 13Y+: -1.18504e-002 -1.94225e-002
- 13Z+: 4.13007e-002 7.67087e-003
- 14X+: -3.55795e-002 1.16708e-003
- 14Y+: -1.68128e-002 -1.82344e-002
- 14Z+: 3.92416e-002 -3.64434e-002
- 15X+: -3.45304e-002 3.78185e-003
- 15Y+: -7.62559e-003 -2.24241e-002
- 15Z+: 6.28286e-003 -1.32711e-002
- 16X+: -9.95646e-003 -6.04395e-003
- 16Y+: -8.73465e-003 -2.20807e-002
- 16Z+: 3.56946e-002 1.69231e-002
- 17X+: -9.32661e-003 -5.51944e-003
- 17Y+: -1.91087e-002 -9.09191e-003
- 17Z+: 4.04981e-002 8.38685e-004
- 18X+: -2.84456e-002 4.02762e-003
- 18Y+: -2.20044e-002 -8.86197e-003
- 18Z+: 4.43051e-002 -5.21033e-002
- 19X+: -3.27019e-002 3.59765e-003
- 19Y+: 2.93163e-003 -2.05064e-002
- 19Z+: -1.77289e-002 -1.29477e-002
- 20X+: -1.08474e-002 -5.78419e-003
- 20Y+: 3.86759e-003 -1.91642e-002
- 20Z+: 2.10135e-002 3.18051e-002
- 3X+: -9.11657e-002 -1.36611e-001
- 3Y+: -1.78165e-001 -3.47193e-002
- 3Z+: 2.37121e-001 -4.96494e-002
- 21X+: -1.34808e-002 -9.69121e-003
- 21Y+: 1.25218e-002 -2.71411e-002
- 21Z+: 2.76673e-001 0.00000e+000
- 22X+: 1.96744e-003 4.90797e-003
- 22Y+: -9.82609e-004 -3.31065e-002
- 22Z+: 1.79246e-001 -3.33238e-002
- 23X+: -1.08728e-002 -8.80278e-003
- 23Z+: 2.30814e-001 -8.33151e-002
- 23Y-: 1.15217e-002 4.01143e-002
-#+end_example
-
-#+begin_src matlab
- mode4 = [...
- -1.02501e-001-j*1.43802e-001, -1.07971e-001+j*5.61418e-004, +1.87145e-001-j*1.03605e-001;
- -9.44764e-002-j*1.36856e-001, -1.04428e-001+j*5.27790e-003, +1.60710e-001-j*7.74212e-002;
- -9.11657e-002-j*1.36611e-001, -1.78165e-001-j*3.47193e-002, +2.37121e-001-j*4.96494e-002;
- -9.17242e-002-j*1.36656e-001, -1.34249e-001-j*1.03884e-002, +1.92123e-001-j*1.25627e-001;
- +1.05875e-002-j*1.03886e-001, -8.26338e-002+j*3.58498e-002, +2.55819e-001-j*6.94290e-003;
- -4.58970e-002-j*1.33904e-002, -9.41660e-002+j*4.99682e-002, +1.28276e-001+j*4.59685e-002;
- -6.01521e-002-j*1.30165e-002, +2.56439e-003-j*6.78141e-002, +5.03428e-002-j*1.59420e-001;
- -1.00895e-002-j*8.80550e-002, +1.26327e-002-j*8.14444e-002, +1.59506e-001-j*2.05360e-001;
- -3.04658e-003-j*1.57921e-001, -8.23501e-002+j*4.82748e-002, +1.69315e-001+j*1.22804e-002;
- -8.25875e-002-j*7.31038e-002, -1.08668e-001+j*3.56364e-002, +8.28567e-002-j*4.49596e-003;
- -1.06792e-001-j*6.95394e-002, +3.77195e-002-j*7.65410e-002, +8.00590e-003-j*2.32461e-002;
- -4.84292e-002-j*1.45790e-001, +1.03862e-002-j*7.31212e-002, +1.78122e-001-j*1.00939e-001;
- -3.49891e-002-j*6.20969e-003, -1.18504e-002-j*1.94225e-002, +4.13007e-002+j*7.67087e-003;
- -3.55795e-002+j*1.16708e-003, -1.68128e-002-j*1.82344e-002, +3.92416e-002-j*3.64434e-002;
- -3.45304e-002+j*3.78185e-003, -7.62559e-003-j*2.24241e-002, +6.28286e-003-j*1.32711e-002;
- -9.95646e-003-j*6.04395e-003, -8.73465e-003-j*2.20807e-002, +3.56946e-002+j*1.69231e-002;
- -9.32661e-003-j*5.51944e-003, -1.91087e-002-j*9.09191e-003, +4.04981e-002+j*8.38685e-004;
- -2.84456e-002+j*4.02762e-003, -2.20044e-002-j*8.86197e-003, +4.43051e-002-j*5.21033e-002;
- -3.27019e-002+j*3.59765e-003, +2.93163e-003-j*2.05064e-002, -1.77289e-002-j*1.29477e-002;
- -1.08474e-002-j*5.78419e-003, +3.86759e-003-j*1.91642e-002, +2.10135e-002+j*3.18051e-002;
- -1.34808e-002-j*9.69121e-003, +1.25218e-002-j*2.71411e-002, +2.76673e-001+j*0.00000e+000;
- +1.96744e-003+j*4.90797e-003, -9.82609e-004-j*3.31065e-002, +1.79246e-001-j*3.33238e-002;
- -1.08728e-002-j*8.80278e-003, -1.15217e-002-j*4.01143e-002, +2.30814e-001-j*8.33151e-002];
-#+end_src
-
-*** All modes
-#+begin_src matlab
-mode_shapes = zeros(23, 3, 10);
-
-mode_shapes(:, :, 1) = [...
--9.34637e-002+j*4.52445e-002, +2.33790e-001+j*1.41439e-003, -1.73754e-002+j*6.02449e-003;
--7.42108e-002+j*3.91543e-002, +2.41566e-001-j*1.44869e-003, -5.99285e-003+j*2.10370e-003;
--9.40720e-002+j*3.93724e-002, +2.52307e-001+j*0.00000e+000, -1.53864e-002-j*9.25720e-004;
--1.02163e-001+j*2.79561e-002, +2.29048e-001+j*2.89782e-002, -2.85130e-002+j*1.77132e-004;
--8.77132e-002+j*3.34081e-002, +2.14182e-001+j*2.14655e-002, -1.54521e-002+j*1.26682e-002;
--7.90143e-002+j*2.42583e-002, +2.20669e-001+j*2.12738e-002, +4.60755e-002+j*4.96406e-003;
--7.79654e-002+j*2.58385e-002, +2.06861e-001+j*3.48019e-002, -1.78311e-002-j*1.29704e-002;
--8.49357e-002+j*3.55200e-002, +2.07470e-001+j*3.59745e-002, -7.66974e-002-j*3.19813e-003;
--7.38565e-002+j*1.95146e-002, +2.17403e-001+j*2.01550e-002, -1.77073e-002-j*3.46414e-003;
--7.77587e-002+j*2.36700e-002, +2.35654e-001-j*2.14540e-002, +7.94165e-002-j*2.45897e-002;
--8.17972e-002+j*2.20583e-002, +2.20906e-001-j*4.30164e-003, -5.60520e-003+j*3.10187e-003;
--8.64261e-002+j*3.66022e-002, +2.15000e-001-j*5.74661e-003, -1.22622e-001+j*4.11767e-002;
--4.25169e-002+j*1.56602e-002, +5.31036e-002-j*1.73951e-002, -4.07130e-002+j*1.26884e-002;
--3.85032e-002+j*1.29431e-002, +5.36716e-002-j*1.80868e-002, +1.00367e-001-j*3.48798e-002;
--4.25524e-002+j*1.46363e-002, +5.19668e-002-j*1.69744e-002, +5.89747e-003-j*2.32428e-003;
--4.31268e-002+j*1.38332e-002, +5.07545e-002-j*1.53045e-002, -1.04172e-001+j*3.17984e-002;
--2.69757e-002+j*9.07955e-003, +3.07837e-002-j*9.44663e-003, -7.63502e-003+j*1.68203e-003;
--3.00097e-002+j*9.23966e-003, +2.83585e-002-j*8.97747e-003, +1.52467e-001-j*4.78675e-002;
--2.70223e-002+j*6.16478e-003, +3.06149e-002-j*6.25382e-003, -4.84888e-003+j*1.93970e-003;
--2.90976e-002+j*7.13184e-003, +3.36738e-002-j*7.30875e-003, -1.66902e-001+j*3.93419e-002;
--7.91940e-002+j*4.39648e-002, +2.04567e-001+j*9.49987e-003, -1.56087e-002+j*7.08838e-003;
--1.01070e-001+j*3.13534e-002, +1.92270e-001+j*1.80423e-002, +2.93053e-003-j*1.97308e-003;
--8.86455e-002+j*4.29906e-002, -3.38351e-002+j*1.81362e-003, +1.90862e-001+j*2.53414e-002];
-
-mode_shapes(:, :, 2) = [...
-+7.56931e-002+j*3.61548e-002, +2.07574e-001+j*1.69205e-004, +1.29733e-002-j*6.78426e-004;
-+8.58732e-002+j*2.54470e-002, +2.07117e-001-j*1.31755e-003, -2.13788e-003-j*1.24974e-002;
-+8.17201e-002+j*2.36079e-002, +2.15927e-001+j*1.61300e-002, -5.48456e-004+j*2.55691e-002;
-+7.09825e-002+j*3.66313e-002, +2.09969e-001+j*1.11484e-002, +9.19478e-003+j*3.47272e-002;
-+6.23935e-002+j*1.02488e-002, +2.30687e-001-j*3.58416e-003, +3.27122e-002-j*5.85468e-002;
-+7.61163e-002-j*2.43630e-002, +2.26743e-001-j*1.15334e-002, -6.20205e-003-j*1.21742e-001;
-+8.01824e-002-j*1.94769e-002, +1.97485e-001+j*4.50105e-002, -2.21170e-002+j*9.77052e-002;
-+6.19294e-002+j*8.15075e-003, +2.03864e-001+j*4.45835e-002, +2.55133e-002+j*1.36137e-001;
-+4.38135e-002+j*7.30537e-002, +2.28426e-001-j*6.58868e-003, +1.16313e-002+j*5.09427e-004;
-+5.45770e-002+j*4.34251e-002, +2.50823e-001+j*0.00000e+000, -4.63460e-002-j*4.76868e-002;
-+5.50987e-002+j*4.26178e-002, +2.29394e-001+j*5.78236e-002, +1.90158e-002+j*1.09139e-002;
-+4.98867e-002+j*7.30190e-002, +2.07871e-001+j*4.57750e-002, +6.69433e-002+j*9.00315e-002;
-+2.48819e-002+j*3.03222e-002, -2.56046e-002-j*3.34132e-002, +2.13260e-002+j*2.58544e-002;
-+2.45706e-002+j*2.60221e-002, -2.57723e-002-j*3.35612e-002, -5.71282e-002-j*6.61562e-002;
-+2.68196e-002+j*2.83888e-002, -2.57263e-002-j*3.29627e-002, -2.11722e-003-j*3.37239e-003;
-+2.51442e-002+j*3.32558e-002, -2.54372e-002-j*3.25062e-002, +5.65780e-002+j*7.64142e-002;
-+1.62437e-002+j*1.94534e-002, -1.31293e-002-j*2.05924e-002, +1.05274e-003+j*3.59474e-003;
-+1.83431e-002+j*2.03836e-002, -1.16818e-002-j*1.86334e-002, -8.66632e-002-j*1.08216e-001;
-+1.62553e-002+j*1.79588e-002, -1.28857e-002-j*1.90512e-002, +6.25653e-003+j*4.97733e-003;
-+1.63830e-002+j*2.03943e-002, -1.48941e-002-j*2.11717e-002, +8.68045e-002+j*1.16491e-001;
-+6.79204e-002-j*5.55513e-002, +2.32871e-001+j*2.33389e-002, +1.34345e-002-j*2.31815e-002;
-+4.02414e-002-j*8.38957e-002, +2.35273e-001+j*2.73256e-002, -8.51632e-003-j*7.49635e-003;
-+6.18293e-002-j*5.99671e-002, +1.63533e-002+j*6.09161e-002, +2.37693e-001+j*4.34204e-002];
-
-mode_shapes(:, :, 3) = [...
-+1.34688e-001-j*6.65071e-002, +1.55316e-002+j*1.01277e-002, -5.88466e-002+j*1.14294e-002;
-+1.53934e-001-j*9.76990e-003, +7.17487e-003+j*1.11925e-002, -4.57205e-002+j*7.26573e-003;
-+1.61551e-001+j*1.65478e-002, -4.12527e-004-j*5.60909e-002, -9.00640e-003+j*3.50754e-003;
-+1.37298e-001-j*5.24661e-002, +1.19427e-003-j*5.39240e-002, -1.25915e-002+j*5.38133e-003;
-+2.43192e-001-j*3.17374e-002, -2.15730e-001-j*7.69941e-004, -1.56268e-001+j*1.44118e-002;
--7.27705e-002-j*3.54943e-003, -2.47706e-001+j*2.66480e-003, -1.21590e-001+j*1.06054e-002;
--7.25870e-002-j*4.62024e-003, +2.27073e-001-j*3.69315e-002, +1.22611e-001-j*6.67337e-003;
-+2.32731e-001-j*2.85516e-002, +2.35389e-001-j*3.81905e-002, +5.35574e-002+j*4.30394e-004;
-+2.64170e-001-j*2.67367e-002, -2.56227e-001+j*3.97957e-005, -1.95398e-001+j*2.23549e-002;
--1.66953e-002-j*7.95698e-003, -2.66547e-001-j*2.17687e-002, +1.56278e-002+j*2.23786e-003;
--3.42364e-002-j*9.30205e-003, +2.52340e-001-j*7.47237e-003, -9.51643e-004+j*3.64798e-003;
-+2.97574e-001+j*0.00000e+000, +2.23170e-001-j*1.37831e-002, +1.06266e-001+j*2.30324e-003;
-+2.67178e-002-j*4.15723e-004, +6.75423e-003-j*2.18428e-003, -1.69423e-002+j*3.12395e-003;
--1.12283e-002+j*2.86316e-004, +5.08225e-003-j*2.14053e-003, +2.18339e-002-j*3.25204e-003;
--1.17948e-002+j*6.82873e-004, +1.94914e-002-j*2.42151e-003, +2.68660e-003-j*2.92104e-004;
-+1.19490e-002+j*1.72236e-005, +1.83552e-002-j*2.71289e-003, -2.70914e-002+j*4.84164e-003;
-+1.00173e-002-j*5.80552e-005, -3.87262e-003-j*1.19607e-003, -8.53809e-003+j*1.48424e-003;
--1.22262e-002+j*5.13096e-004, -5.73905e-003-j*1.07659e-003, +3.51730e-002-j*6.13814e-003;
--1.43735e-002-j*4.78552e-004, +2.31135e-002-j*6.30554e-004, +1.80171e-003-j*1.98835e-004;
-+9.17792e-003+j*5.36661e-004, +2.18969e-002-j*5.81759e-004, -3.72117e-002+j*5.35813e-003;
-+3.38754e-002-j*3.38703e-002, -2.20843e-002+j*2.78581e-002, -8.79541e-002-j*3.67473e-003;
-+3.93064e-002+j*4.69476e-002, -1.69132e-002-j*1.04606e-002, -1.85351e-002+j*1.33750e-003;
-+3.60396e-002-j*2.46238e-002, +3.57722e-003+j*3.64827e-003, -1.92038e-002-j*6.65895e-002];
-
-mode_shapes(:, :, 4) = [...
--1.02501e-001-j*1.43802e-001, -1.07971e-001+j*5.61418e-004, +1.87145e-001-j*1.03605e-001;
--9.44764e-002-j*1.36856e-001, -1.04428e-001+j*5.27790e-003, +1.60710e-001-j*7.74212e-002;
--9.11657e-002-j*1.36611e-001, -1.78165e-001-j*3.47193e-002, +2.37121e-001-j*4.96494e-002;
--9.17242e-002-j*1.36656e-001, -1.34249e-001-j*1.03884e-002, +1.92123e-001-j*1.25627e-001;
-+1.05875e-002-j*1.03886e-001, -8.26338e-002+j*3.58498e-002, +2.55819e-001-j*6.94290e-003;
--4.58970e-002-j*1.33904e-002, -9.41660e-002+j*4.99682e-002, +1.28276e-001+j*4.59685e-002;
--6.01521e-002-j*1.30165e-002, +2.56439e-003-j*6.78141e-002, +5.03428e-002-j*1.59420e-001;
--1.00895e-002-j*8.80550e-002, +1.26327e-002-j*8.14444e-002, +1.59506e-001-j*2.05360e-001;
--3.04658e-003-j*1.57921e-001, -8.23501e-002+j*4.82748e-002, +1.69315e-001+j*1.22804e-002;
--8.25875e-002-j*7.31038e-002, -1.08668e-001+j*3.56364e-002, +8.28567e-002-j*4.49596e-003;
--1.06792e-001-j*6.95394e-002, +3.77195e-002-j*7.65410e-002, +8.00590e-003-j*2.32461e-002;
--4.84292e-002-j*1.45790e-001, +1.03862e-002-j*7.31212e-002, +1.78122e-001-j*1.00939e-001;
--3.49891e-002-j*6.20969e-003, -1.18504e-002-j*1.94225e-002, +4.13007e-002+j*7.67087e-003;
--3.55795e-002+j*1.16708e-003, -1.68128e-002-j*1.82344e-002, +3.92416e-002-j*3.64434e-002;
--3.45304e-002+j*3.78185e-003, -7.62559e-003-j*2.24241e-002, +6.28286e-003-j*1.32711e-002;
--9.95646e-003-j*6.04395e-003, -8.73465e-003-j*2.20807e-002, +3.56946e-002+j*1.69231e-002;
--9.32661e-003-j*5.51944e-003, -1.91087e-002-j*9.09191e-003, +4.04981e-002+j*8.38685e-004;
--2.84456e-002+j*4.02762e-003, -2.20044e-002-j*8.86197e-003, +4.43051e-002-j*5.21033e-002;
--3.27019e-002+j*3.59765e-003, +2.93163e-003-j*2.05064e-002, -1.77289e-002-j*1.29477e-002;
--1.08474e-002-j*5.78419e-003, +3.86759e-003-j*1.91642e-002, +2.10135e-002+j*3.18051e-002;
--1.34808e-002-j*9.69121e-003, +1.25218e-002-j*2.71411e-002, +2.76673e-001+j*0.00000e+000;
-+1.96744e-003+j*4.90797e-003, -9.82609e-004-j*3.31065e-002, +1.79246e-001-j*3.33238e-002;
--1.08728e-002-j*8.80278e-003, +2.30814e-001-j*8.33151e-002, -1.15217e-002-j*4.01143e-002];
-
-mode_shapes(:, :, 5) = [...
-+3.55328e-001+j*0.00000e+000, +6.67612e-002+j*5.48020e-002, +3.03237e-002+j*5.29473e-004;
-+3.16372e-001-j*3.84091e-002, +5.27472e-002+j*5.88474e-002, +2.86305e-002-j*1.74805e-002;
-+3.00803e-001-j*1.36309e-002, +7.04883e-002+j*1.24492e-001, +7.23329e-002+j*2.33738e-002;
-+3.32527e-001-j*2.26876e-004, +9.82263e-002+j*1.20397e-001, +9.86580e-002+j*3.55048e-002;
-+4.96498e-002+j*2.31008e-002, +9.79716e-002+j*1.42500e-002, -1.15121e-001-j*3.59085e-002;
-+1.41924e-001+j*2.16209e-002, +8.76030e-002+j*6.39650e-003, -8.75727e-002-j*3.71261e-002;
-+1.41522e-001+j*1.96964e-002, -1.01959e-001+j*4.10992e-004, +2.14744e-001+j*4.91249e-002;
-+4.33170e-002+j*1.84481e-002, -8.24640e-002+j*3.42475e-003, +2.32281e-001+j*5.40699e-002;
-+1.47782e-001+j*4.93091e-002, +8.75397e-002+j*7.75318e-004, -6.80833e-002-j*9.72902e-003;
-+2.00055e-001+j*3.81689e-002, +8.06886e-002+j*1.19008e-002, -1.40810e-002-j*1.12625e-002;
-+1.96526e-001+j*3.87737e-002, -8.42766e-002+j*9.20233e-003, +1.02951e-001+j*3.37680e-002;
-+1.25035e-001+j*4.67796e-002, -8.81307e-002+j*5.81039e-004, +7.94320e-002+j*2.19736e-002;
-+2.03946e-002+j*2.50162e-002, +7.93788e-002-j*1.40794e-002, -4.15470e-002+j*4.95855e-004;
-+6.56876e-002-j*2.14826e-002, +8.21523e-002-j*1.94792e-002, +3.44089e-002+j*2.32727e-003;
-+5.98960e-002-j*2.17160e-002, +4.74914e-002+j*2.31386e-002, +3.58704e-002+j*1.13591e-003;
-+1.91580e-002+j*2.15329e-002, +5.14631e-002+j*1.70019e-002, -3.90820e-002-j*9.20853e-003;
-+8.98876e-003+j*2.56390e-002, +7.93497e-002-j*2.34846e-002, -5.61039e-002-j*3.03271e-003;
-+5.72051e-002-j*2.29477e-002, +8.76985e-002-j*2.73606e-002, +5.13896e-002+j*8.58341e-003;
-+6.71099e-002-j*2.67997e-002, +1.80119e-002+j*4.02601e-002, +6.40092e-002+j*7.11273e-003;
-+1.48349e-002+j*2.57533e-002, +1.35189e-002+j*3.69351e-002, -3.31024e-002-j*1.65471e-002;
-+2.52156e-002-j*4.65138e-003, +7.94380e-004+j*1.56790e-002, +1.01067e-002-j*3.35468e-003;
-+3.30841e-002+j*6.73531e-003, +1.69827e-004+j*9.48996e-003, +8.16746e-002+j*1.39885e-002;
-+2.91404e-002-j*2.43138e-003, +1.38761e-001+j*3.67410e-002, -4.17833e-003+j*8.35629e-004];
-
-mode_shapes(:, :, 6) = [...
-+3.76055e-001-j*2.00477e-002, -2.18528e-002-j*2.46738e-001, -2.01369e-002-j*2.48481e-002;
-+3.73870e-001-j*6.46353e-002, -3.66940e-002-j*2.49113e-001, -9.20410e-002-j*2.72520e-002;
-+3.71070e-001-j*4.42411e-003, +5.79596e-002-j*2.58311e-001, +2.62275e-003+j*9.26708e-003;
-+3.82440e-001+j*0.00000e+000, +3.30266e-002-j*2.08256e-001, +7.22558e-002+j*1.47204e-002;
--3.73785e-003+j*3.81592e-002, +4.74482e-002+j*5.41354e-002, -5.78227e-002-j*8.70215e-002;
-+6.08721e-002+j*7.20835e-002, +5.73258e-002+j*5.38176e-002, -3.34121e-002-j*8.54509e-002;
-+5.96968e-002+j*8.31733e-002, -7.64618e-002-j*4.19504e-002, +3.48953e-002+j*4.79635e-002;
--1.41532e-003+j*3.79318e-002, -6.79853e-002-j*3.88324e-002, +6.64542e-002+j*9.20955e-002;
-+2.96044e-002+j*7.83613e-002, +4.91378e-002+j*4.74080e-002, -2.15758e-002-j*5.51292e-002;
-+3.52566e-002+j*1.00976e-001, +4.16302e-002+j*5.95793e-002, -1.83944e-002-j*5.09313e-002;
-+3.49287e-002+j*1.10404e-001, -5.46487e-002-j*3.95054e-002, +1.88545e-002+j*3.82156e-002;
-+1.70173e-002+j*8.68762e-002, -5.52511e-002-j*4.46179e-002, +7.63555e-003+j*6.17646e-002;
--8.22469e-004-j*1.81402e-002, -1.96193e-003-j*2.76646e-002, -1.97033e-003+j*1.06615e-002;
--1.16438e-003-j*2.68725e-002, -1.11909e-003-j*2.38894e-002, +1.50332e-003+j*1.31644e-002;
--1.77060e-003-j*2.77807e-002, -1.01121e-003-j*2.37147e-002, -2.45798e-003-j*1.41886e-002;
--1.85500e-003-j*2.20304e-002, -4.77462e-004-j*2.19932e-002, -6.85097e-003-j*7.04903e-003;
--6.77197e-004-j*1.56812e-002, -2.19412e-003-j*2.65284e-002, +3.96653e-004+j*2.95178e-002;
--1.14513e-003-j*1.99551e-002, -2.35828e-003-j*2.88909e-002, +3.70211e-003+j*2.02423e-002;
--1.16798e-003-j*2.31638e-002, -4.75969e-004-j*2.23413e-002, -2.07031e-003-j*3.41651e-002;
--1.99807e-004-j*2.09301e-002, -2.40560e-004-j*1.78264e-002, -9.91090e-003-j*3.12664e-002;
-+9.69966e-003+j*2.95222e-002, -1.19231e-002+j*5.23077e-003, -9.79113e-003-j*4.50715e-002;
-+1.36018e-002+j*2.24850e-002, -9.79427e-003+j*9.84679e-003, +2.18456e-002-j*1.57858e-002;
-+1.09214e-002+j*2.93115e-002, +2.43859e-002+j*3.35745e-002, -1.07735e-002+j*1.21178e-002];
-
-mode_shapes(:, :, 7) = [...
-+4.18739e-001-j*2.21696e-002, +6.52636e-002-j*1.29498e-001, -1.90337e-002+j*9.61505e-003;
-+4.27024e-001-j*3.03566e-002, +4.22791e-002-j*1.32892e-001, -1.65941e-002+j*2.17638e-002;
-+4.66694e-001+j*1.38778e-017, +7.51273e-002-j*1.57468e-001, -2.91618e-002+j*4.11516e-002;
-+4.18867e-001+j*2.39590e-002, +7.51007e-002-j*1.13378e-001, -7.11238e-003+j*2.72692e-002;
--3.26299e-002+j*2.12910e-002, -4.80710e-002+j*8.82799e-002, +5.82558e-002-j*9.16159e-002;
--4.61031e-002+j*8.08300e-002, -2.80650e-002+j*7.37925e-002, +3.54903e-002-j*3.02341e-002;
--5.14543e-002+j*7.23863e-002, +1.91387e-002-j*7.65710e-002, -3.92182e-002+j*5.06089e-002;
--3.35647e-002+j*2.16695e-002, +1.88798e-002-j*6.19822e-002, -5.08508e-002+j*8.78653e-002;
--4.93941e-002+j*6.46940e-002, -2.90637e-002+j*7.66360e-002, +5.24626e-002-j*6.16359e-002;
--5.85364e-002+j*5.59044e-002, -2.63581e-002+j*5.43466e-002, +2.90174e-002-j*3.98049e-002;
--6.07978e-002+j*5.54585e-002, +3.16828e-002-j*8.54810e-002, -3.44914e-002-j*4.03684e-003;
--6.18120e-002+j*7.90821e-002, +2.38807e-002-j*5.62399e-002, -5.04609e-002+j*3.27008e-002;
-+1.57670e-002-j*3.20728e-003, -5.98007e-003-j*3.10416e-003, -1.67104e-003-j*1.59089e-003;
-+1.79638e-002-j*7.40235e-003, -8.20109e-003-j*2.36675e-004, -1.69812e-003+j*1.67596e-003;
-+1.87809e-002-j*8.55724e-003, -2.81069e-003-j*3.03393e-003, -5.71319e-003-j*2.26161e-003;
-+1.88829e-002-j*8.50228e-003, -5.28373e-003-j*2.52386e-003, -1.48737e-002-j*5.08140e-003;
-+2.28380e-002-j*7.51769e-003, -7.57170e-003-j*2.75553e-003, -6.10380e-003+j*5.15562e-003;
-+2.08600e-002-j*6.11732e-003, -4.73105e-003-j*3.30979e-003, -2.51369e-003+j*5.42921e-003;
-+2.00008e-002-j*5.92617e-003, -3.50988e-003-j*4.55853e-003, -5.43701e-003-j*6.57229e-003;
-+2.28149e-002-j*8.22905e-003, -4.83167e-003-j*3.10509e-003, -2.10958e-002-j*1.33421e-002;
--1.83145e-002+j*2.76844e-002, +5.61668e-003-j*1.41226e-002, +2.20876e-002-j*2.27446e-002;
--5.42112e-003+j*2.22444e-002, -4.20426e-005-j*8.78901e-003, +5.54714e-003+j*2.71564e-002;
--1.70108e-002+j*2.83751e-002, -1.44473e-002+j*4.50880e-002, -5.26736e-003-j*5.75716e-003];
-
-mode_shapes(:, :, 8) = [...
--1.40928e-001+j*1.28570e-001, +2.95471e-001-j*1.35692e-001, -6.61656e-002+j*2.95705e-002;
--1.56673e-001+j*5.19030e-002, +3.08231e-001-j*1.41453e-001, -9.70918e-002+j*4.95018e-002;
--1.72505e-001+j*2.26273e-002, +3.97224e-001-j*2.77556e-017, -1.29223e-001+j*4.47412e-002;
--1.69978e-001+j*1.16284e-001, +3.37516e-001+j*7.69873e-003, -8.49480e-002+j*2.17071e-002;
-+5.38303e-004-j*3.59916e-003, -6.72455e-002-j*2.06230e-002, +2.66448e-002+j*4.10505e-002;
--7.96526e-003-j*7.76851e-002, -2.63530e-002-j*3.75474e-002, -1.05984e-001+j*9.32474e-002;
-+4.72518e-002-j*1.00199e-001, -5.50664e-002+j*1.50246e-001, -8.50976e-002+j*2.78531e-002;
-+7.58419e-003-j*8.61594e-003, -9.02101e-002+j*1.58224e-001, +6.03081e-002-j*1.24162e-001;
-+2.99027e-002-j*5.27128e-002, -8.80464e-002-j*2.99113e-004, +9.02851e-002-j*3.99771e-002;
-+3.23132e-002-j*5.87278e-002, +3.81174e-002-j*3.69992e-002, +1.16643e-002+j*6.21068e-002;
-+5.79795e-002-j*8.33565e-002, -1.22448e-003+j*8.81473e-002, +8.40150e-002-j*1.16264e-002;
-+1.35399e-002-j*3.80303e-002, -9.58200e-002+j*1.46531e-001, +1.06769e-001-j*8.97034e-002;
-+5.34299e-004+j*1.35179e-002, +8.71327e-004-j*6.41448e-003, +3.33208e-002-j*2.12545e-002;
--2.79263e-004+j*5.08578e-003, -1.45476e-003-j*7.65161e-003, +6.98235e-002-j*2.45395e-002;
--9.22822e-005+j*7.03205e-003, -5.62836e-003-j*2.79991e-003, +3.99717e-002-j*8.30891e-003;
-+1.87833e-002+j*3.26772e-003, -4.86774e-003-j*4.32297e-003, +5.97375e-002-j*1.77542e-002;
-+1.14169e-002+j*5.70930e-003, -8.23489e-003-j*4.53684e-003, +3.14016e-002-j*2.50637e-002;
-+1.15995e-003+j*5.79180e-003, -6.69740e-003-j*4.66433e-003, +8.17695e-002-j*2.78384e-002;
-+5.23838e-004+j*6.46432e-003, +3.36104e-003-j*4.42572e-003, +3.64589e-002+j*5.74796e-004;
-+1.57042e-002+j*5.94177e-003, -1.49670e-003-j*4.22955e-003, +8.68520e-002-j*1.43981e-002;
-+8.00706e-004-j*2.91734e-002, +1.20708e-002+j*4.24081e-002, -5.91796e-002+j*4.00346e-002;
--1.91799e-003-j*1.37294e-002, +9.85285e-003+j*3.17934e-002, -1.78010e-001+j*7.91267e-002;
-+3.57271e-003-j*3.09959e-002, -5.77781e-002-j*1.27957e-002, +1.31025e-002+j*1.92303e-002];
-
-mode_shapes(:, :, 9) = [...
-+1.58897e-002+j*3.23763e-002, -1.23332e-001-j*3.20376e-002, +6.78860e-002-j*1.28743e-002;
-+5.67179e-003+j*4.26539e-002, -1.20726e-001-j*4.15603e-002, +7.66846e-002-j*1.24290e-002;
-+2.24198e-002+j*3.45953e-002, -1.03213e-001-j*4.97049e-002, +5.49175e-002-j*5.50883e-003;
-+2.68792e-002+j*2.97222e-002, -1.17598e-001-j*3.13791e-002, +5.59736e-002-j*1.71122e-002;
-+1.39733e-002-j*1.56260e-002, +1.43952e-001+j*2.28119e-002, -4.56377e-003+j*4.88790e-002;
--2.18507e-002-j*1.25664e-002, +6.15387e-002-j*6.31793e-003, +3.05342e-002+j*3.24595e-002;
--7.85412e-003-j*1.85600e-002, +1.25733e-001+j*1.77063e-002, +5.34635e-002+j*4.72260e-003;
--1.10454e-002-j*2.13217e-002, +1.26440e-001+j*1.96001e-002, -5.62624e-002-j*1.07192e-002;
-+5.84467e-003-j*4.07134e-002, +5.16711e-003+j*4.70857e-002, -1.93010e-001+j*6.79213e-003;
-+5.31962e-002-j*1.11322e-002, +3.23294e-001-j*2.12981e-002, +2.14310e-001+j*4.85898e-003;
--2.44580e-002-j*1.33220e-002, +4.08800e-001+j*2.09082e-002, +5.11454e-001+j*0.00000e+000;
--2.51332e-002-j*1.42719e-003, +8.97105e-002+j*4.85852e-002, -1.27426e-001-j*9.59723e-003;
--2.08176e-003+j*1.37185e-002, -3.99530e-002+j*2.11895e-002, -1.17813e-001+j*7.60972e-002;
--1.34824e-002+j*7.11258e-003, -4.19473e-002+j*1.83590e-002, -2.07198e-002-j*2.51991e-002;
--6.84747e-003+j*8.45921e-003, -3.33872e-002+j*1.71496e-002, +6.99867e-002-j*6.93158e-002;
--2.64313e-002+j*5.08903e-003, -3.03569e-002+j*1.29946e-002, -1.39115e-001+j*5.72459e-002;
--2.90186e-002+j*1.48257e-002, -5.55429e-002+j*2.74156e-002, -1.62035e-001+j*8.04187e-002;
--2.05855e-002+j*1.11922e-002, -6.58789e-002+j*3.20524e-002, -1.02263e-002-j*4.24087e-002;
--1.40204e-002+j*8.01102e-003, -5.72647e-002+j*2.37484e-002, +1.75053e-001-j*9.63667e-002;
--3.50818e-002+j*1.41152e-002, -5.19701e-002+j*2.31951e-002, -1.15951e-001+j*2.91582e-002;
--5.78005e-003-j*7.05841e-003, +8.29016e-002+j*1.36984e-002, +4.03470e-003+j*4.03325e-002;
--1.39928e-002-j*1.14088e-002, +8.05288e-002+j*1.51031e-002, +1.12255e-002+j*3.21224e-002;
--1.02276e-002-j*8.35724e-003, -4.89246e-003+j*1.67800e-002, +7.80514e-002+j*1.53467e-002];
-
-mode_shapes(:, :, 10) = [...
-+3.33349e-002-j*4.89606e-003, -8.67138e-002-j*1.69402e-002, +2.87366e-002-j*1.66842e-002;
-+2.95730e-002-j*6.10477e-004, -9.24590e-002-j*1.92562e-002, +5.21162e-002-j*1.31811e-002;
-+3.26966e-002+j*1.03975e-002, -8.55682e-002-j*4.71847e-002, +3.99404e-002+j*8.59358e-003;
-+3.45452e-002-j*3.05951e-003, -7.73823e-002-j*2.32199e-002, +2.30960e-002-j*7.49928e-003;
--3.72461e-003-j*5.40336e-003, +1.80151e-001-j*1.42898e-002, -8.63921e-003+j*1.95638e-002;
--1.11285e-002-j*2.22175e-003, +6.92355e-002-j*1.24144e-002, +8.02097e-002-j*6.81531e-003;
--2.99885e-002-j*4.21951e-004, +8.19709e-002+j*1.22484e-002, +3.97531e-002+j*1.33874e-002;
--1.59231e-002-j*3.96929e-003, +9.31295e-002+j*9.75532e-003, -4.01947e-002-j*5.17841e-003;
--7.32828e-003-j*2.93496e-002, +4.39909e-002+j*1.25298e-002, -8.87525e-002+j*2.05359e-002;
-+8.20167e-002+j*6.86693e-004, +4.25475e-001-j*2.36494e-002, +3.37034e-001-j*2.44199e-002;
--2.68694e-002+j*3.82921e-003, +4.79292e-001+j*1.35903e-002, +5.06762e-001+j*0.00000e+000;
-+1.40565e-002-j*5.41957e-003, +1.17563e-001+j*2.50398e-002, -5.97219e-002+j*5.92813e-004;
-+2.30939e-002+j*1.16755e-002, +4.11136e-003+j*1.65726e-002, +2.41863e-002+j*5.06658e-002;
--4.92960e-003+j*9.24082e-003, -5.44667e-003+j*1.41983e-002, -3.73537e-002-j*1.87263e-002;
-+9.68682e-003+j*1.11791e-002, -5.13436e-003+j*1.29205e-002, -4.88765e-002-j*4.97821e-002;
--1.66711e-003+j*1.03280e-002, +9.57955e-004+j*1.28350e-002, +3.30268e-002+j*5.44211e-002;
-+5.90540e-003+j*1.67113e-002, +1.34280e-002+j*2.62111e-002, +4.38613e-002+j*7.17028e-002;
-+4.97752e-003+j*1.47634e-002, +1.56773e-002+j*3.16026e-002, -5.27493e-002-j*3.38315e-002;
-+2.83485e-003+j*1.14816e-002, +9.80676e-003+j*2.51504e-002, -6.78645e-002-j*9.90875e-002;
-+5.62294e-003+j*1.84035e-002, +1.03717e-002+j*2.37801e-002, +2.58497e-002+j*3.75352e-002;
--8.75236e-003-j*4.71723e-003, +6.99107e-002+j*1.51894e-002, +3.46273e-002+j*1.48547e-002;
--1.72822e-002-j*8.75192e-003, +6.96759e-002+j*1.59783e-002, +8.07917e-002+j*1.97809e-002;
--1.29601e-002-j*5.61834e-003, +1.76126e-002+j*4.62761e-003, +6.64667e-002+j*1.61199e-002];
-#+end_src
-
-** Define a point for each solid body
-We define accelerometer indices used to define the motion of each solid body (2 3-axis accelerometer are enough).
-#+begin_src matlab
- stages = [17, 19; % Bottom Granite
- 13, 15; % Top Granite
- 9, 11; % Ty
- 5, 7; % Ry
- 21, 22; % Spindle
- 1, 3]; % Hexapod
-#+end_src
-
-We define the origin point ${}^AO_B$ of the solid body $\{B\}$.
-Here we choose the middle point between the two accelerometers.
-This could be define differently (for instance by choosing the center of mass).
-#+begin_src matlab
- AOB = zeros(3, size(stages, 1));
-
- for i = 1:size(stages, 1)
- AOB(:, i) = mean(positions(stages(i, :), 1:3))';
- end
-#+end_src
-
-Then we compute the positions of the sensors with respect to the previously defined origin for the frame $\{B\}$: ${}^BP_1$ and ${}^BP_2$.
-#+begin_src matlab
- BP1 = zeros(3, size(stages, 1));
- BP2 = zeros(3, size(stages, 1));
-
- for i = 1:size(stages, 1)
- BP1(:, i) = positions(stages(i, 1), 1:3)' - AOB(:, i);
- BP2(:, i) = positions(stages(i, 2), 1:3)' - AOB(:, i);
- end
-#+end_src
-
-Let's define one absolute frame $\{A\}$ and one frame $\{B\}$ fixed w.r.t. the solid body.
-We note ${}^AO_B$ the position of origin of $\{B\}$ expressed in $\{A\}$.
-
-We are measuring with the accelerometers the absolute motion of points $P_1$ and $P_2$: ${}^Av_{P_1}$ and ${}^Av_{P_2}$.
-
-Let's note ${}^BP_1$ and ${}^BP_2$ the (known) coordinates of $P_1$ and $P_2$ expressed in the frame $\{B\}$.
-
-Then we have:
-\begin{align}
- {}^Av_{P_1} &= {}^Av_{O_B} + {}^A\Omega^\times {}^AR_B {}^BP_1 \\
- {}^Av_{P_2} &= {}^Av_{O_B} + {}^A\Omega^\times {}^AR_B {}^BP_2
-\end{align}
-
-And we obtain
-\begin{align}
- {}^A\Omega^\times {}^AR_B &= \left( {}^Av_{P_2} - {}^Av_{P_1} \right) \left( {}^BP_2 - {}^BP_1 \right)^{-1}\\
- {}^Av_{O_B} &= {}^Av_{P_1} - \left( {}^Av_{P_2} - {}^Av_{P_1} \right) \left( {}^BP_2 - {}^BP_1 \right)^{-1} {}^BP_1
-\end{align}
-
-#+begin_src matlab
- AVOB = zeros(3, size(stages, 1));
- ARB = zeros(3, 3, size(stages, 1));
- for i = 1:size(stages, 1)
- AVOB(:, i) = mode1(stages(i, 1), :)' - (mode1(stages(i, 2), :)' - mode1(stages(i, 1), :)')*pinv(BP2(:, i) - BP1(:, i))*BP1(:, i);
- ARB(:, :, i) = (mode1(stages(i, 2), :)' - mode1(stages(i, 1), :)')*pinv(BP2(:, i) - BP1(:, i));
- end
-#+end_src
-
-** Argand Diagram
-For mode 1
-
-#+begin_src matlab
- figure;
- hold on;
- for i=1:size(mode1, 1)
- plot([0, real(mode1(i, 1))], [0, imag(mode1(i, 1))], '-k')
- plot([0, real(mode1(i, 2))], [0, imag(mode1(i, 2))], '-k')
- plot([0, real(mode1(i, 3))], [0, imag(mode1(i, 3))], '-k')
-
- % plot([0, real(mode2(i, 1))], [0, imag(mode2(i, 1))], '-r')
- % plot([0, real(mode2(i, 2))], [0, imag(mode2(i, 2))], '-r')
- % plot([0, real(mode2(i, 3))], [0, imag(mode2(i, 3))], '-r')
-
- % plot([0, real(mode3(i, 1))], [0, imag(mode3(i, 1))], '-b')
- % plot([0, real(mode3(i, 2))], [0, imag(mode3(i, 2))], '-b')
- % plot([0, real(mode3(i, 3))], [0, imag(mode3(i, 3))], '-b')
- end
-
- for i=1:size(AVOB, 2)
- plot([0, real(AVOB(1, i))], [0, imag(AVOB(1, i))], '-r')
- plot([0, real(AVOB(2, i))], [0, imag(AVOB(2, i))], '-r')
- plot([0, real(AVOB(3, i))], [0, imag(AVOB(3, i))], '-r')
- end
-
- % ang=0:0.01:2*pi;
- % radius1 = max(max(sqrt(real(mode1).^2+imag(mode1).^2)));
- % plot(radius1*cos(ang), radius1*sin(ang), '-k');
-
- % radius2 = max(max(sqrt(real(mode2).^2+imag(mode2).^2)));
- % plot(radius2*cos(ang), radius2*sin(ang), '-r');
-
- % radius3 = max(max(sqrt(real(mode3).^2+imag(mode3).^2)));
- % plot(radius3*cos(ang), radius3*sin(ang), '-b');
-
- hold off;
- axis manual equal
-#+end_src
-
-** TEST: animate first mode
-#+begin_src matlab
- figure;
- hold on;
- fill3(positions(1:4, 1), positions(1:4, 2), positions(1:4, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(5:8, 1), positions(5:8, 2), positions(5:8, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(9:12, 1), positions(9:12, 2), positions(9:12, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(13:16, 1), positions(13:16, 2), positions(13:16, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(17:20, 1), positions(17:20, 2), positions(17:20, 3), 'k', 'FaceAlpha', 0.5)
- fill3(positions(21:23, 1), positions(21:23, 2), positions(21:23, 3), 'k', 'FaceAlpha', 0.5)
- hold off;
-#+end_src
-
-#+NAME: fig:mode_shapes
-#+HEADER: :tangle no :exports results :results value file raw replace :noweb yes
-#+begin_src matlab
- rec = polyshape([-2 -2 2 2],[-3 3 3 -3]);
- h = figure;
- filename = 'figs/mode_shapes.gif';
- n = 20;
-
- for i = 1:n
- axis manual equal
-
- Dm = real(V(1:3, 5)*cos(2*pi*i/n));
- rec_i = rotate(rec, 180/pi*Dm(3));
- rec_i = translate(rec_i, 10*Dm(1), 10*Dm(2));
- plot(rec_i);
-
- xlim([-3, 3]); ylim([-4, 4]);
-
- set(h, 'visible', 'off');
- set(h, 'pos', [0, 0, 500, 500]);
- drawnow;
-
- % Capture the plot as an image
- frame = getframe(h);
- im = frame2im(frame);
- [imind,cm] = rgb2ind(im,256);
-
- % Write to the GIF File
- if i == 1
- imwrite(imind,cm,filename,'gif','DelayTime',0.1,'Loopcount',inf);
- else
- imwrite(imind,cm,filename,'gif','DelayTime',0.1,'WriteMode','append');
+ meas_dir = meas.(sprintf('FFT1_H1_%i_1_RpName', j))(end);
+ meas_sign = meas.(sprintf('FFT1_H1_%i_1_RpName', j))(end-1);
+ % Determine what is the correct measurement sign
+ meas_factor = str2num([meas_sign, '1']);
+ if meas_dir ~= 'Z'
+ meas_factor = meas_factor*(-1);
end
- end
- set(h, 'visible', 'on');
- ans = filename;
+ % FRFs(acc_i+n_acc*(find(dirs==meas_dir)-1), find(dirs==exc_dir), :) = exc_factor*meas_factor*meas.(sprintf('FFT1_H1_%i_1_Y_ReIm', j));
+ % COHs(acc_i+n_acc*(find(dirs==meas_dir)-1), find(dirs==exc_dir), :) = meas.(sprintf('FFT1_Coh_%i_1_RMS_Y_Val', j));
+
+ FRFs(find(dirs==meas_dir)+3*(acc_i-1), find(dirs==exc_dir), :) = exc_factor*meas_factor*meas.(sprintf('FFT1_H1_%i_1_Y_ReIm', j));
+ COHs(find(dirs==meas_dir)+3*(acc_i-1), find(dirs==exc_dir), :) = meas.(sprintf('FFT1_Coh_%i_1_RMS_Y_Val', j));
+ end
+ end
+ freqs = meas.FFT1_Coh_10_1_RMS_X_Val;
#+end_src
-** From 6 translations to translation + rotation
-Let's define one absolute frame $\{A\}$ and one frame $\{B\}$ fixed w.r.t. the solid body.
-We note ${}^AO_B$ the position of origin of $\{B\}$ expressed in $\{A\}$.
-
-We are measuring with the accelerometers the absolute motion of points $P_1$ and $P_2$: ${}^AP_1$ and ${}^AP_2$.
-
-Let's note ${}^BP_1$ and ${}^BP_2$ the (known) coordinates of $P_1$ and $P_2$ expressed in the frame $\{B\}$.
-
-Then we have:
-\begin{align}
- {}^AP_1 &= {}^AO_B + {}^AR_B {}^BP_1 \\
- {}^AP_2 &= {}^AO_B + {}^AR_B {}^BP_2
-\end{align}
-
-And we obtain
-\begin{align}
- {}^AR_B &= \left( {}^AP_2 - {}^AP_1 \right) \left( {}^BP_2 - {}^BP_1 \right)^{-1}\\
- {}^AO_B &= {}^Av_{P_1} - \left( {}^AP_2 - {}^AP_1 \right) \left( {}^BP_2 - {}^BP_1 \right)^{-1} {}^BP_1
-\end{align}
-
-* Problem with AirLoc System
-4 Airloc Levelers are used for the granite (figure [[fig:airloc]]).
-
-#+name: fig:airloc
-#+caption: AirLoc used for the granite (2120-KSKC)
-#+attr_html: :width 500px
-[[file:img/airloc/IMG_20190618_155522.jpg]]
-
-They are probably *not well leveled* so that could explain the first modes at 11Hz and 17Hz.
+And we save the obtained FRF matrix and Coherence matrix in a =.mat= file.
+#+begin_src matlab
+ save('./mat/frf_coh_matrices.mat', 'FRFs', 'COHs', 'freqs');
+#+end_src
diff --git a/modal-analysis/modal_extraction.org b/modal-analysis/modal_extraction.org
index b8bdc0a..6071586 100644
--- a/modal-analysis/modal_extraction.org
+++ b/modal-analysis/modal_extraction.org
@@ -7,7 +7,7 @@
#+AUTHOR: Dehaeze Thomas
#+HTML_LINK_HOME: ../index.html
-#+HTML_LINK_UP: ../index.html
+#+HTML_LINK_UP: ./index.html
#+HTML_HEAD:
#+HTML_HEAD:
@@ -48,6 +48,1160 @@
<>
#+end_src
+
+
+* TODO After that, this should be in the modal extraction
+* TODO Part to explain how to choose the modes
+* Obtained Mode Shapes animations
+One all the FRFs are obtained, we can estimate the modal parameters (resonance frequencies, modal shapes and modal damping) within the modal software.
+
+For that, multiple modal extraction techniques can be used (SIMO, MIMO, narrow band, wide band, ...).
+
+Then, it is possible to show the modal shapes with an animation.
+
+Examples are shown on figures [[fig:mode1]] and [[fig:mode6]].
+
+Animations of all the other modes are accessible using the following links: [[file:img/modes/mode1.gif][mode 1]], [[file:img/modes/mode2.gif][mode 2]], [[file:img/modes/mode3.gif][mode 3]], [[file:img/modes/mode4.gif][mode 4]], [[file:img/modes/mode5.gif][mode 5]], [[file:img/modes/mode6.gif][mode 6]], [[file:img/modes/mode7.gif][mode 7]], [[file:img/modes/mode8.gif][mode 8]], [[file:img/modes/mode9.gif][mode 9]], [[file:img/modes/mode10.gif][mode 10]], [[file:img/modes/mode11.gif][mode 11]], [[file:img/modes/mode12.gif][mode 12]], [[file:img/modes/mode13.gif][mode 13]], [[file:img/modes/mode14.gif][mode 14]], [[file:img/modes/mode15.gif][mode 15]], [[file:img/modes/mode16.gif][mode 16]], [[file:img/modes/mode17.gif][mode 17]], [[file:img/modes/mode18.gif][mode 18]], [[file:img/modes/mode19.gif][mode 19]], [[file:img/modes/mode20.gif][mode 20]], [[file:img/modes/mode21.gif][mode 21]].
+
+#+name: fig:mode1
+#+caption: Mode 1
+[[file:img/modes/mode1.gif]]
+
+#+name: fig:mode6
+#+caption: Mode 6
+[[file:img/modes/mode6.gif]]
+
+* Obtained Modal Parameters
+From the modal analysis software, we can export the obtained modal parameters:
+- the resonance frequencies
+- the modes shapes
+- the modal damping
+- the residues
+
+These can be express as the *eigen matrices*:
+\[ \Omega = \begin{bmatrix}
+ \omega_1^2 & & 0 \\
+ & \ddots & \\
+ 0 & & \omega_n^2
+\end{bmatrix}; \quad \Psi = \begin{bmatrix}
+ & & \\
+ \{\psi_1\} & \dots & \{\psi_n\} \\
+ & &
+\end{bmatrix} \]
+where $\bar{\omega}_r^2$ is the $r^\text{th}$ eigenvalue squared and $\{\phi\}_r$ is a description of the corresponding *mode shape*.
+
+The file containing the modal parameters is =mat/modes.asc=. Its first 20 lines as shown below.
+
+#+begin_src bash :results output :exports results :eval no-export
+ sed 20q mat/modes.asc | sed $'s/\r//'
+#+end_src
+
+#+RESULTS:
+#+begin_example
+Created by N-Modal
+Estimator: bbfd
+01-Jul-19 16:44:11
+
+
+Mode 1
+freq = 11.41275Hz
+damp = 8.72664%
+modal A = -4.50556e+003-9.41744e+003i
+modal B = -7.00928e+005+2.62922e+005i
+Mode matrix of local coordinate [DOF: Re IM]
+ 1X-: -1.04114e-001 3.50664e-002
+ 1Y-: 2.34008e-001 5.04273e-004
+ 1Z+: -1.93303e-002 5.08614e-003
+ 2X-: -8.38439e-002 3.45978e-002
+ 2Y-: 2.42440e-001 0.00000e+000
+ 2Z+: -7.40734e-003 5.17734e-003
+ 3Y-: 2.17655e-001 6.10802e-003
+ 3X+: 1.18685e-001 -3.54602e-002
+ 3Z+: -2.37725e-002 -1.61649e-003
+#+end_example
+
+We split this big =modes.asc= file into sub text files using =bash=. The obtained files are described one table [[tab:modes_files]].
+
+#+begin_src bash :results none
+ sed '/^\s*[0-9]*[XYZ][+-]:/!d' mat/modes.asc > mat/mode_shapes.txt
+ sed '/freq/!d' mat/modes.asc | sed 's/.* = \(.*\)Hz/\1/' > mat/mode_freqs.txt
+ sed '/damp/!d' mat/modes.asc | sed 's/.* = \(.*\)\%/\1/' > mat/mode_damps.txt
+ sed '/modal A/!d' mat/modes.asc | sed 's/.* =\s\+\([-0-9.e]\++[0-9]\+\)\([-+0-9.e]\+\)i/\1 \2/' > mat/mode_modal_a.txt
+ sed '/modal B/!d' mat/modes.asc | sed 's/.* =\s\+\([-0-9.e]\++[0-9]\+\)\([-+0-9.e]\+\)i/\1 \2/' > mat/mode_modal_b.txt
+#+end_src
+
+#+name: tab:modes_files
+#+caption: Split =modes.asc= file
+| Filename | Content |
+|------------------------+--------------------------------------------------|
+| =mat/mode_shapes.txt= | mode shapes |
+| =mat/mode_freqs.txt= | resonance frequencies |
+| =mat/mode_damps.txt= | modal damping |
+| =mat/mode_modal_a.txt= | modal residues at low frequency (to be checked) |
+| =mat/mode_modal_b.txt= | modal residues at high frequency (to be checked) |
+
+Then we import the obtained =.txt= files on Matlab using =readtable= function.
+#+begin_src matlab
+ shapes = readtable('mat/mode_shapes.txt', 'ReadVariableNames', false); % [Sign / Real / Imag]
+ freqs = table2array(readtable('mat/mode_freqs.txt', 'ReadVariableNames', false)); % in [Hz]
+ damps = table2array(readtable('mat/mode_damps.txt', 'ReadVariableNames', false)); % in [%]
+ modal_a = table2array(readtable('mat/mode_modal_a.txt', 'ReadVariableNames', false)); % [Real / Imag]
+ modal_b = table2array(readtable('mat/mode_modal_b.txt', 'ReadVariableNames', false)); % [Real / Imag]
+
+ modal_a = complex(modal_a(:, 1), modal_a(:, 2));
+ modal_b = complex(modal_b(:, 1), modal_b(:, 2));
+#+end_src
+
+We guess the number of modes identified from the length of the imported data.
+#+begin_src matlab
+ acc_n = 23; % Number of accelerometers
+ dir_n = 3; % Number of directions
+ dirs = 'XYZ';
+
+ mod_n = size(shapes,1)/acc_n/dir_n; % Number of modes
+#+end_src
+
+As the mode shapes are split into 3 parts (direction plus sign, real part and imaginary part), we aggregate them into one array of complex numbers.
+#+begin_src matlab
+ T_sign = table2array(shapes(:, 1));
+ T_real = table2array(shapes(:, 2));
+ T_imag = table2array(shapes(:, 3));
+
+ modes = zeros(mod_n, acc_n, dir_n);
+
+ for mod_i = 1:mod_n
+ for acc_i = 1:acc_n
+ % Get the correct section of the signs
+ T = T_sign(acc_n*dir_n*(mod_i-1)+1:acc_n*dir_n*mod_i);
+ for dir_i = 1:dir_n
+ % Get the line corresponding to the sensor
+ i = find(contains(T, sprintf('%i%s',acc_i, dirs(dir_i))), 1, 'first')+acc_n*dir_n*(mod_i-1);
+ modes(mod_i, acc_i, dir_i) = str2num([T_sign{i}(end-1), '1'])*complex(T_real(i),T_imag(i));
+ end
+ end
+ end
+#+end_src
+
+The obtained mode frequencies and damping are shown below.
+#+begin_src matlab :exports both :results value table replace :post addhdr(*this*)
+ data2orgtable([freqs, damps], {}, {'Frequency [Hz]', 'Damping [%]'}, ' %.1f ');
+#+end_src
+
+#+RESULTS:
+| Frequency [Hz] | Damping [%] |
+|----------------+-------------|
+| 11.4 | 8.7 |
+| 18.5 | 11.8 |
+| 37.6 | 6.4 |
+| 39.4 | 3.6 |
+| 54.0 | 0.2 |
+| 56.1 | 2.8 |
+| 69.7 | 4.6 |
+| 71.6 | 0.6 |
+| 72.4 | 1.6 |
+| 84.9 | 3.6 |
+| 90.6 | 0.3 |
+| 91.0 | 2.9 |
+| 95.8 | 3.3 |
+| 105.4 | 3.3 |
+| 106.8 | 1.9 |
+| 112.6 | 3.0 |
+| 116.8 | 2.7 |
+| 124.1 | 0.6 |
+| 145.4 | 1.6 |
+| 150.1 | 2.2 |
+| 164.7 | 1.4 |
+
+* Compute the Modal Model
+** Matlab Init :noexport:ignore:
+#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
+ <>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+ <>
+#+end_src
+
+** Position of the accelerometers
+There are 23 accelerometers:
+- 4 on the bottom granite
+- 4 on the top granite
+- 4 on top of the translation stage
+- 4 on the tilt stage
+- 3 on top of the spindle
+- 4 on top of the hexapod
+
+The coordinates defined in the software are displayed below.
+
+#+begin_src bash :results output :exports results :eval no-export
+ sed -n 18,40p modal_analysis/acc_coordinates.txt | tac --
+#+end_src
+
+#+RESULTS:
+#+begin_example
+ 1 1.0000e-001 1.0000e-001 1.1500e+000 0 Top
+ 2 1.0000e-001 -1.0000e-001 1.1500e+000 0 Top
+ 3 -1.0000e-001 -1.0000e-001 1.1500e+000 0 Top
+ 4 -1.0000e-001 1.0000e-001 1.1500e+000 0 Top
+ 5 4.0000e-001 4.0000e-001 9.5000e-001 0 inner
+ 6 4.0000e-001 -4.0000e-001 9.5000e-001 0 inner
+ 7 -4.0000e-001 -4.0000e-001 9.5000e-001 0 inner
+ 8 -4.0000e-001 4.0000e-001 9.5000e-001 0 inner
+ 9 5.0000e-001 5.0000e-001 9.0000e-001 0 outer
+ 10 5.0000e-001 -5.0000e-001 9.0000e-001 0 outer
+ 11 -5.0000e-001 -5.0000e-001 9.0000e-001 0 outer
+ 12 -5.0000e-001 5.0000e-001 9.0000e-001 0 outer
+ 13 5.5000e-001 5.5000e-001 5.5000e-001 0 top
+ 14 5.5000e-001 -5.5000e-001 5.5000e-001 0 top
+ 15 -5.5000e-001 -5.5000e-001 5.5000e-001 0 top
+ 16 -5.5000e-001 5.5000e-001 5.5000e-001 0 top
+ 17 9.5000e-001 9.5000e-001 4.0000e-001 0 low
+ 18 9.5000e-001 -9.5000e-001 4.0000e-001 0 low
+ 19 -9.5000e-001 -9.5000e-001 4.0000e-001 0 low
+ 20 -9.5000e-001 9.5000e-001 4.0000e-001 0 low
+ 21 2.0000e-001 2.0000e-001 8.5000e-001 0 bot
+ 22 0.0000e+000 -2.0000e-001 8.5000e-001 0 bot
+ 23 -2.0000e-001 2.0000e-001 8.5000e-001 0 bot
+#+end_example
+
+#+name: tab:acc_location
+#+caption: Location of each Accelerometer (using the normal coordinate frame with X aligned with the X ray)
+| *Node number* | *Solid Body* | *Location* | *X* | *Y* | *Z* |
+|---------------+-------------------+------------+-------+-------+------|
+| 1 | Hexapod - Top | -X/-Y | -0.10 | -0.10 | 1.15 |
+| 2 | | -X/+Y | -0.10 | 0.10 | 1.15 |
+| 3 | | +X/+Y | 0.10 | 0.10 | 1.15 |
+| 4 | | +X/-Y | 0.10 | -0.10 | 1.15 |
+|---------------+-------------------+------------+-------+-------+------|
+| 5 | Tilt - Top | -X/-Y | -0.40 | -0.40 | 0.95 |
+| 6 | | -X/+Y | -0.40 | 0.40 | 0.95 |
+| 7 | | +X/+Y | 0.40 | 0.40 | 0.95 |
+| 8 | | +X/-Y | 0.40 | -0.40 | 0.95 |
+|---------------+-------------------+------------+-------+-------+------|
+| 9 | Translation - Top | -X/-Y | -0.50 | -0.50 | 0.90 |
+| 10 | | -X/+Y | -0.50 | 0.50 | 0.90 |
+| 11 | | +X/+Y | 0.50 | 0.50 | 0.90 |
+| 12 | | +X/-Y | 0.50 | -0.50 | 0.90 |
+|---------------+-------------------+------------+-------+-------+------|
+| 13 | Top Granite | -X/-Y | -0.55 | -0.50 | 0.55 |
+| 14 | | -X/+Y | -0.55 | 0.50 | 0.55 |
+| 15 | | +X/+Y | 0.55 | 0.50 | 0.55 |
+| 16 | | +X/-Y | 0.55 | -0.50 | 0.55 |
+|---------------+-------------------+------------+-------+-------+------|
+| 17 | Bottom Granite | -X/-Y | -0.95 | -0.90 | 0.40 |
+| 18 | | -X/+Y | -0.95 | 0.90 | 0.40 |
+| 19 | | +X/+Y | 0.95 | 0.90 | 0.40 |
+| 20 | | +X/-Y | 0.95 | -0.90 | 0.40 |
+|---------------+-------------------+------------+-------+-------+------|
+| 21 | Spindle - Top | -X/-Y | -0.20 | -0.20 | 0.85 |
+| 22 | | +0/+Y | 0.00 | 0.20 | 0.85 |
+| 23 | | +X/-Y | 0.20 | -0.20 | 0.85 |
+
+** Define positions of the accelerometers on matlab
+We define the X-Y-Z position of each sensor.
+Each line corresponds to one accelerometer, X-Y-Z position in meter.
+#+begin_src matlab
+ positions = [...
+ -0.10, -0.10, 1.15 ; ...
+ -0.10, 0.10, 1.15 ; ...
+ 0.10, 0.10, 1.15 ; ...
+ 0.10, -0.10, 1.15 ; ...
+ -0.40, -0.40, 0.95 ; ...
+ -0.40, 0.40, 0.95 ; ...
+ 0.40, 0.40, 0.95 ; ...
+ 0.40, -0.40, 0.95 ; ...
+ -0.50, -0.50, 0.90 ; ...
+ -0.50, 0.50, 0.90 ; ...
+ 0.50, 0.50, 0.90 ; ...
+ 0.50, -0.50, 0.90 ; ...
+ -0.55, -0.50, 0.55 ; ...
+ -0.55, 0.50, 0.55 ; ...
+ 0.55, 0.50, 0.55 ; ...
+ 0.55, -0.50, 0.55 ; ...
+ -0.95, -0.90, 0.40 ; ...
+ -0.95, 0.90, 0.40 ; ...
+ 0.95, 0.90, 0.40 ; ...
+ 0.95, -0.90, 0.40 ; ...
+ -0.20, -0.20, 0.85 ; ...
+ 0.00, 0.20, 0.85 ; ...
+ 0.20, -0.20, 0.85 ];
+#+end_src
+
+
+#+begin_src matlab
+ figure;
+ hold on;
+ fill3(positions(1:4, 1), positions(1:4, 2), positions(1:4, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(5:8, 1), positions(5:8, 2), positions(5:8, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(9:12, 1), positions(9:12, 2), positions(9:12, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(13:16, 1), positions(13:16, 2), positions(13:16, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(17:20, 1), positions(17:20, 2), positions(17:20, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(21:23, 1), positions(21:23, 2), positions(21:23, 3), 'k', 'FaceAlpha', 0.5)
+ hold off;
+#+end_src
+
+** Import the modal vectors on matlab
+*** Mode1
+#+begin_src bash :results output :exports none :eval no-export
+ sed -n 12,80p modal_analysis/modes_propres_narband.asc
+#+end_src
+
+#+RESULTS:
+#+begin_example
+ 1X+: -9.34637e-002 4.52445e-002
+ 1Y+: 2.33790e-001 1.41439e-003
+ 1Z+: -1.73754e-002 6.02449e-003
+ 2X+: -7.42108e-002 3.91543e-002
+ 2Y+: 2.41566e-001 -1.44869e-003
+ 2Z+: -5.99285e-003 2.10370e-003
+ 4X+: -1.02163e-001 2.79561e-002
+ 4Y+: 2.29048e-001 2.89782e-002
+ 4Z+: -2.85130e-002 1.77132e-004
+ 5X+: -8.77132e-002 3.34081e-002
+ 5Y+: 2.14182e-001 2.14655e-002
+ 5Z+: -1.54521e-002 1.26682e-002
+ 6X+: -7.90143e-002 2.42583e-002
+ 6Y+: 2.20669e-001 2.12738e-002
+ 6Z+: 4.60755e-002 4.96406e-003
+ 7X+: -7.79654e-002 2.58385e-002
+ 7Y+: 2.06861e-001 3.48019e-002
+ 7Z+: -1.78311e-002 -1.29704e-002
+ 8X+: -8.49357e-002 3.55200e-002
+ 8Y+: 2.07470e-001 3.59745e-002
+ 8Z+: -7.66974e-002 -3.19813e-003
+ 9X+: -7.38565e-002 1.95146e-002
+ 9Y+: 2.17403e-001 2.01550e-002
+ 9Z+: -1.77073e-002 -3.46414e-003
+ 10X+: -7.77587e-002 2.36700e-002
+ 10Y+: 2.35654e-001 -2.14540e-002
+ 10Z+: 7.94165e-002 -2.45897e-002
+ 11X+: -8.17972e-002 2.20583e-002
+ 11Y+: 2.20906e-001 -4.30164e-003
+ 11Z+: -5.60520e-003 3.10187e-003
+ 12X+: -8.64261e-002 3.66022e-002
+ 12Y+: 2.15000e-001 -5.74661e-003
+ 12Z+: -1.22622e-001 4.11767e-002
+ 13X+: -4.25169e-002 1.56602e-002
+ 13Y+: 5.31036e-002 -1.73951e-002
+ 13Z+: -4.07130e-002 1.26884e-002
+ 14X+: -3.85032e-002 1.29431e-002
+ 14Y+: 5.36716e-002 -1.80868e-002
+ 14Z+: 1.00367e-001 -3.48798e-002
+ 15X+: -4.25524e-002 1.46363e-002
+ 15Y+: 5.19668e-002 -1.69744e-002
+ 15Z+: 5.89747e-003 -2.32428e-003
+ 16X+: -4.31268e-002 1.38332e-002
+ 16Y+: 5.07545e-002 -1.53045e-002
+ 16Z+: -1.04172e-001 3.17984e-002
+ 17X+: -2.69757e-002 9.07955e-003
+ 17Y+: 3.07837e-002 -9.44663e-003
+ 17Z+: -7.63502e-003 1.68203e-003
+ 18X+: -3.00097e-002 9.23966e-003
+ 18Y+: 2.83585e-002 -8.97747e-003
+ 18Z+: 1.52467e-001 -4.78675e-002
+ 19X+: -2.70223e-002 6.16478e-003
+ 19Y+: 3.06149e-002 -6.25382e-003
+ 19Z+: -4.84888e-003 1.93970e-003
+ 20X+: -2.90976e-002 7.13184e-003
+ 20Y+: 3.36738e-002 -7.30875e-003
+ 20Z+: -1.66902e-001 3.93419e-002
+ 3X+: -9.40720e-002 3.93724e-002
+ 3Y+: 2.52307e-001 0.00000e+000
+ 3Z+: -1.53864e-002 -9.25720e-004
+ 21X+: -7.91940e-002 4.39648e-002
+ 21Y+: 2.04567e-001 9.49987e-003
+ 21Z+: -1.56087e-002 7.08838e-003
+ 22X+: -1.01070e-001 3.13534e-002
+ 22Y+: 1.92270e-001 1.80423e-002
+ 22Z+: 2.93053e-003 -1.97308e-003
+ 23X+: -8.86455e-002 4.29906e-002
+ 23Z+: -3.38351e-002 1.81362e-003
+ 23Y-: -1.90862e-001 -2.53414e-002
+#+end_example
+
+#+begin_src matlab
+ mode1 = [...
+ -9.34637e-002+j*4.52445e-002, +2.33790e-001+j*1.41439e-003, -1.73754e-002+j*6.02449e-003;
+ -7.42108e-002+j*3.91543e-002, +2.41566e-001-j*1.44869e-003, -5.99285e-003+j*2.10370e-003;
+ -9.40720e-002+j*3.93724e-002, +2.52307e-001+j*0.00000e+000, -1.53864e-002-j*9.25720e-004;
+ -1.02163e-001+j*2.79561e-002, +2.29048e-001+j*2.89782e-002, -2.85130e-002+j*1.77132e-004;
+ -8.77132e-002+j*3.34081e-002, +2.14182e-001+j*2.14655e-002, -1.54521e-002+j*1.26682e-002;
+ -7.90143e-002+j*2.42583e-002, +2.20669e-001+j*2.12738e-002, +4.60755e-002+j*4.96406e-003;
+ -7.79654e-002+j*2.58385e-002, +2.06861e-001+j*3.48019e-002, -1.78311e-002-j*1.29704e-002;
+ -8.49357e-002+j*3.55200e-002, +2.07470e-001+j*3.59745e-002, -7.66974e-002-j*3.19813e-003;
+ -7.38565e-002+j*1.95146e-002, +2.17403e-001+j*2.01550e-002, -1.77073e-002-j*3.46414e-003;
+ -7.77587e-002+j*2.36700e-002, +2.35654e-001-j*2.14540e-002, +7.94165e-002-j*2.45897e-002;
+ -8.17972e-002+j*2.20583e-002, +2.20906e-001-j*4.30164e-003, -5.60520e-003+j*3.10187e-003;
+ -8.64261e-002+j*3.66022e-002, +2.15000e-001-j*5.74661e-003, -1.22622e-001+j*4.11767e-002;
+ -4.25169e-002+j*1.56602e-002, +5.31036e-002-j*1.73951e-002, -4.07130e-002+j*1.26884e-002;
+ -3.85032e-002+j*1.29431e-002, +5.36716e-002-j*1.80868e-002, +1.00367e-001-j*3.48798e-002;
+ -4.25524e-002+j*1.46363e-002, +5.19668e-002-j*1.69744e-002, +5.89747e-003-j*2.32428e-003;
+ -4.31268e-002+j*1.38332e-002, +5.07545e-002-j*1.53045e-002, -1.04172e-001+j*3.17984e-002;
+ -2.69757e-002+j*9.07955e-003, +3.07837e-002-j*9.44663e-003, -7.63502e-003+j*1.68203e-003;
+ -3.00097e-002+j*9.23966e-003, +2.83585e-002-j*8.97747e-003, +1.52467e-001-j*4.78675e-002;
+ -2.70223e-002+j*6.16478e-003, +3.06149e-002-j*6.25382e-003, -4.84888e-003+j*1.93970e-003;
+ -2.90976e-002+j*7.13184e-003, +3.36738e-002-j*7.30875e-003, -1.66902e-001+j*3.93419e-002;
+ -7.91940e-002+j*4.39648e-002, +2.04567e-001+j*9.49987e-003, -1.56087e-002+j*7.08838e-003;
+ -1.01070e-001+j*3.13534e-002, +1.92270e-001+j*1.80423e-002, +2.93053e-003-j*1.97308e-003;
+ -8.86455e-002+j*4.29906e-002, +1.90862e-001+j*2.53414e-002, -3.38351e-002+j*1.81362e-003];
+#+end_src
+
+*** Mode2
+#+begin_src bash :results output :exports none :eval no-export
+ sed -n 88,156p modal_analysis/modes_propres_narband.asc
+#+end_src
+
+#+RESULTS:
+#+begin_example
+ 1X+: 7.56931e-002 3.61548e-002
+ 1Y+: 2.07574e-001 1.69205e-004
+ 1Z+: 1.29733e-002 -6.78426e-004
+ 2X+: 8.58732e-002 2.54470e-002
+ 2Y+: 2.07117e-001 -1.31755e-003
+ 2Z+: -2.13788e-003 -1.24974e-002
+ 4X+: 7.09825e-002 3.66313e-002
+ 4Y+: 2.09969e-001 1.11484e-002
+ 4Z+: 9.19478e-003 3.47272e-002
+ 5X+: 6.23935e-002 1.02488e-002
+ 5Y+: 2.30687e-001 -3.58416e-003
+ 5Z+: 3.27122e-002 -5.85468e-002
+ 6X+: 7.61163e-002 -2.43630e-002
+ 6Y+: 2.26743e-001 -1.15334e-002
+ 6Z+: -6.20205e-003 -1.21742e-001
+ 7X+: 8.01824e-002 -1.94769e-002
+ 7Y+: 1.97485e-001 4.50105e-002
+ 7Z+: -2.21170e-002 9.77052e-002
+ 8X+: 6.19294e-002 8.15075e-003
+ 8Y+: 2.03864e-001 4.45835e-002
+ 8Z+: 2.55133e-002 1.36137e-001
+ 9X+: 4.38135e-002 7.30537e-002
+ 9Y+: 2.28426e-001 -6.58868e-003
+ 9Z+: 1.16313e-002 5.09427e-004
+ 10X+: 5.45770e-002 4.34251e-002
+ 10Y+: 2.50823e-001 0.00000e+000
+ 10Z+: -4.63460e-002 -4.76868e-002
+ 11X+: 5.50987e-002 4.26178e-002
+ 11Y+: 2.29394e-001 5.78236e-002
+ 11Z+: 1.90158e-002 1.09139e-002
+ 12X+: 4.98867e-002 7.30190e-002
+ 12Y+: 2.07871e-001 4.57750e-002
+ 12Z+: 6.69433e-002 9.00315e-002
+ 13X+: 2.48819e-002 3.03222e-002
+ 13Y+: -2.56046e-002 -3.34132e-002
+ 13Z+: 2.13260e-002 2.58544e-002
+ 14X+: 2.45706e-002 2.60221e-002
+ 14Y+: -2.57723e-002 -3.35612e-002
+ 14Z+: -5.71282e-002 -6.61562e-002
+ 15X+: 2.68196e-002 2.83888e-002
+ 15Y+: -2.57263e-002 -3.29627e-002
+ 15Z+: -2.11722e-003 -3.37239e-003
+ 16X+: 2.51442e-002 3.32558e-002
+ 16Y+: -2.54372e-002 -3.25062e-002
+ 16Z+: 5.65780e-002 7.64142e-002
+ 17X+: 1.62437e-002 1.94534e-002
+ 17Y+: -1.31293e-002 -2.05924e-002
+ 17Z+: 1.05274e-003 3.59474e-003
+ 18X+: 1.83431e-002 2.03836e-002
+ 18Y+: -1.16818e-002 -1.86334e-002
+ 18Z+: -8.66632e-002 -1.08216e-001
+ 19X+: 1.62553e-002 1.79588e-002
+ 19Y+: -1.28857e-002 -1.90512e-002
+ 19Z+: 6.25653e-003 4.97733e-003
+ 20X+: 1.63830e-002 2.03943e-002
+ 20Y+: -1.48941e-002 -2.11717e-002
+ 20Z+: 8.68045e-002 1.16491e-001
+ 3X+: 8.17201e-002 2.36079e-002
+ 3Y+: 2.15927e-001 1.61300e-002
+ 3Z+: -5.48456e-004 2.55691e-002
+ 21X+: 6.79204e-002 -5.55513e-002
+ 21Y+: 2.32871e-001 2.33389e-002
+ 21Z+: 1.34345e-002 -2.31815e-002
+ 22X+: 4.02414e-002 -8.38957e-002
+ 22Y+: 2.35273e-001 2.73256e-002
+ 22Z+: -8.51632e-003 -7.49635e-003
+ 23X+: 6.18293e-002 -5.99671e-002
+ 23Z+: 1.63533e-002 6.09161e-002
+ 23Y-: -2.37693e-001 -4.34204e-002
+#+end_example
+
+#+begin_src matlab
+ mode2 = [...
+ +7.56931e-002+j*3.61548e-002, +2.07574e-001+j*1.69205e-004, +1.29733e-002-j*6.78426e-004;
+ +8.58732e-002+j*2.54470e-002, +2.07117e-001-j*1.31755e-003, -2.13788e-003-j*1.24974e-002;
+ +8.17201e-002+j*2.36079e-002, +2.15927e-001+j*1.61300e-002, -5.48456e-004+j*2.55691e-002;
+ +7.09825e-002+j*3.66313e-002, +2.09969e-001+j*1.11484e-002, +9.19478e-003+j*3.47272e-002;
+ +6.23935e-002+j*1.02488e-002, +2.30687e-001-j*3.58416e-003, +3.27122e-002-j*5.85468e-002;
+ +7.61163e-002-j*2.43630e-002, +2.26743e-001-j*1.15334e-002, -6.20205e-003-j*1.21742e-001;
+ +8.01824e-002-j*1.94769e-002, +1.97485e-001+j*4.50105e-002, -2.21170e-002+j*9.77052e-002;
+ +6.19294e-002+j*8.15075e-003, +2.03864e-001+j*4.45835e-002, +2.55133e-002+j*1.36137e-001;
+ +4.38135e-002+j*7.30537e-002, +2.28426e-001-j*6.58868e-003, +1.16313e-002+j*5.09427e-004;
+ +5.45770e-002+j*4.34251e-002, +2.50823e-001+j*0.00000e+000, -4.63460e-002-j*4.76868e-002;
+ +5.50987e-002+j*4.26178e-002, +2.29394e-001+j*5.78236e-002, +1.90158e-002+j*1.09139e-002;
+ +4.98867e-002+j*7.30190e-002, +2.07871e-001+j*4.57750e-002, +6.69433e-002+j*9.00315e-002;
+ +2.48819e-002+j*3.03222e-002, -2.56046e-002-j*3.34132e-002, +2.13260e-002+j*2.58544e-002;
+ +2.45706e-002+j*2.60221e-002, -2.57723e-002-j*3.35612e-002, -5.71282e-002-j*6.61562e-002;
+ +2.68196e-002+j*2.83888e-002, -2.57263e-002-j*3.29627e-002, -2.11722e-003-j*3.37239e-003;
+ +2.51442e-002+j*3.32558e-002, -2.54372e-002-j*3.25062e-002, +5.65780e-002+j*7.64142e-002;
+ +1.62437e-002+j*1.94534e-002, -1.31293e-002-j*2.05924e-002, +1.05274e-003+j*3.59474e-003;
+ +1.83431e-002+j*2.03836e-002, -1.16818e-002-j*1.86334e-002, -8.66632e-002-j*1.08216e-001;
+ +1.62553e-002+j*1.79588e-002, -1.28857e-002-j*1.90512e-002, +6.25653e-003+j*4.97733e-003;
+ +1.63830e-002+j*2.03943e-002, -1.48941e-002-j*2.11717e-002, +8.68045e-002+j*1.16491e-001;
+ +6.79204e-002-j*5.55513e-002, +2.32871e-001+j*2.33389e-002, +1.34345e-002-j*2.31815e-002;
+ +4.02414e-002-j*8.38957e-002, +2.35273e-001+j*2.73256e-002, -8.51632e-003-j*7.49635e-003;
+ +6.18293e-002-j*5.99671e-002, +2.37693e-001+j*4.34204e-002, +1.63533e-002+j*6.09161e-002]
+#+end_src
+
+*** Mode3
+#+begin_src bash :results output :exports none :eval no-export
+ sed -n 164,232p modal_analysis/modes_propres_narband.asc
+#+end_src
+
+#+RESULTS:
+#+begin_example
+ 1X+: 1.34688e-001 -6.65071e-002
+ 1Y+: 1.55316e-002 1.01277e-002
+ 1Z+: -5.88466e-002 1.14294e-002
+ 2X+: 1.53934e-001 -9.76990e-003
+ 2Y+: 7.17487e-003 1.11925e-002
+ 2Z+: -4.57205e-002 7.26573e-003
+ 4X+: 1.37298e-001 -5.24661e-002
+ 4Y+: 1.19427e-003 -5.39240e-002
+ 4Z+: -1.25915e-002 5.38133e-003
+ 5X+: 2.43192e-001 -3.17374e-002
+ 5Y+: -2.15730e-001 -7.69941e-004
+ 5Z+: -1.56268e-001 1.44118e-002
+ 6X+: -7.27705e-002 -3.54943e-003
+ 6Y+: -2.47706e-001 2.66480e-003
+ 6Z+: -1.21590e-001 1.06054e-002
+ 7X+: -7.25870e-002 -4.62024e-003
+ 7Y+: 2.27073e-001 -3.69315e-002
+ 7Z+: 1.22611e-001 -6.67337e-003
+ 8X+: 2.32731e-001 -2.85516e-002
+ 8Y+: 2.35389e-001 -3.81905e-002
+ 8Z+: 5.35574e-002 4.30394e-004
+ 9X+: 2.64170e-001 -2.67367e-002
+ 9Y+: -2.56227e-001 3.97957e-005
+ 9Z+: -1.95398e-001 2.23549e-002
+ 10X+: -1.66953e-002 -7.95698e-003
+ 10Y+: -2.66547e-001 -2.17687e-002
+ 10Z+: 1.56278e-002 2.23786e-003
+ 11X+: -3.42364e-002 -9.30205e-003
+ 11Y+: 2.52340e-001 -7.47237e-003
+ 11Z+: -9.51643e-004 3.64798e-003
+ 12X+: 2.97574e-001 0.00000e+000
+ 12Y+: 2.23170e-001 -1.37831e-002
+ 12Z+: 1.06266e-001 2.30324e-003
+ 13X+: 2.67178e-002 -4.15723e-004
+ 13Y+: 6.75423e-003 -2.18428e-003
+ 13Z+: -1.69423e-002 3.12395e-003
+ 14X+: -1.12283e-002 2.86316e-004
+ 14Y+: 5.08225e-003 -2.14053e-003
+ 14Z+: 2.18339e-002 -3.25204e-003
+ 15X+: -1.17948e-002 6.82873e-004
+ 15Y+: 1.94914e-002 -2.42151e-003
+ 15Z+: 2.68660e-003 -2.92104e-004
+ 16X+: 1.19490e-002 1.72236e-005
+ 16Y+: 1.83552e-002 -2.71289e-003
+ 16Z+: -2.70914e-002 4.84164e-003
+ 17X+: 1.00173e-002 -5.80552e-005
+ 17Y+: -3.87262e-003 -1.19607e-003
+ 17Z+: -8.53809e-003 1.48424e-003
+ 18X+: -1.22262e-002 5.13096e-004
+ 18Y+: -5.73905e-003 -1.07659e-003
+ 18Z+: 3.51730e-002 -6.13814e-003
+ 19X+: -1.43735e-002 -4.78552e-004
+ 19Y+: 2.31135e-002 -6.30554e-004
+ 19Z+: 1.80171e-003 -1.98835e-004
+ 20X+: 9.17792e-003 5.36661e-004
+ 20Y+: 2.18969e-002 -5.81759e-004
+ 20Z+: -3.72117e-002 5.35813e-003
+ 3X+: 1.61551e-001 1.65478e-002
+ 3Y+: -4.12527e-004 -5.60909e-002
+ 3Z+: -9.00640e-003 3.50754e-003
+ 21X+: 3.38754e-002 -3.38703e-002
+ 21Y+: -2.20843e-002 2.78581e-002
+ 21Z+: -8.79541e-002 -3.67473e-003
+ 22X+: 3.93064e-002 4.69476e-002
+ 22Y+: -1.69132e-002 -1.04606e-002
+ 22Z+: -1.85351e-002 1.33750e-003
+ 23X+: 3.60396e-002 -2.46238e-002
+ 23Z+: 3.57722e-003 3.64827e-003
+ 23Y-: 1.92038e-002 6.65895e-002
+#+end_example
+
+#+begin_src matlab
+ mode3 = [...
+ +1.34688e-001-j*6.65071e-002, +1.55316e-002+j*1.01277e-002, -5.88466e-002+j*1.14294e-002;
+ +1.53934e-001-j*9.76990e-003, +7.17487e-003+j*1.11925e-002, -4.57205e-002+j*7.26573e-003;
+ +1.61551e-001+j*1.65478e-002, -4.12527e-004-j*5.60909e-002, -9.00640e-003+j*3.50754e-003;
+ +1.37298e-001-j*5.24661e-002, +1.19427e-003-j*5.39240e-002, -1.25915e-002+j*5.38133e-003;
+ +2.43192e-001-j*3.17374e-002, -2.15730e-001-j*7.69941e-004, -1.56268e-001+j*1.44118e-002;
+ -7.27705e-002-j*3.54943e-003, -2.47706e-001+j*2.66480e-003, -1.21590e-001+j*1.06054e-002;
+ -7.25870e-002-j*4.62024e-003, +2.27073e-001-j*3.69315e-002, +1.22611e-001-j*6.67337e-003;
+ +2.32731e-001-j*2.85516e-002, +2.35389e-001-j*3.81905e-002, +5.35574e-002+j*4.30394e-004;
+ +2.64170e-001-j*2.67367e-002, -2.56227e-001+j*3.97957e-005, -1.95398e-001+j*2.23549e-002;
+ -1.66953e-002-j*7.95698e-003, -2.66547e-001-j*2.17687e-002, +1.56278e-002+j*2.23786e-003;
+ -3.42364e-002-j*9.30205e-003, +2.52340e-001-j*7.47237e-003, -9.51643e-004+j*3.64798e-003;
+ +2.97574e-001+j*0.00000e+000, +2.23170e-001-j*1.37831e-002, +1.06266e-001+j*2.30324e-003;
+ +2.67178e-002-j*4.15723e-004, +6.75423e-003-j*2.18428e-003, -1.69423e-002+j*3.12395e-003;
+ -1.12283e-002+j*2.86316e-004, +5.08225e-003-j*2.14053e-003, +2.18339e-002-j*3.25204e-003;
+ -1.17948e-002+j*6.82873e-004, +1.94914e-002-j*2.42151e-003, +2.68660e-003-j*2.92104e-004;
+ +1.19490e-002+j*1.72236e-005, +1.83552e-002-j*2.71289e-003, -2.70914e-002+j*4.84164e-003;
+ +1.00173e-002-j*5.80552e-005, -3.87262e-003-j*1.19607e-003, -8.53809e-003+j*1.48424e-003;
+ -1.22262e-002+j*5.13096e-004, -5.73905e-003-j*1.07659e-003, +3.51730e-002-j*6.13814e-003;
+ -1.43735e-002-j*4.78552e-004, +2.31135e-002-j*6.30554e-004, +1.80171e-003-j*1.98835e-004;
+ +9.17792e-003+j*5.36661e-004, +2.18969e-002-j*5.81759e-004, -3.72117e-002+j*5.35813e-003;
+ +3.38754e-002-j*3.38703e-002, -2.20843e-002+j*2.78581e-002, -8.79541e-002-j*3.67473e-003;
+ +3.93064e-002+j*4.69476e-002, -1.69132e-002-j*1.04606e-002, -1.85351e-002+j*1.33750e-003;
+ +3.60396e-002-j*2.46238e-002, -1.92038e-002-j*6.65895e-002, +3.57722e-003+j*3.64827e-003];
+#+end_src
+
+*** Mode4
+#+begin_src bash :results output :exports none :eval no-export
+ sed -n 240,308p modal_analysis/modes_propres_narband.asc
+#+end_src
+
+#+RESULTS:
+#+begin_example
+ 1X+: -1.02501e-001 -1.43802e-001
+ 1Y+: -1.07971e-001 5.61418e-004
+ 1Z+: 1.87145e-001 -1.03605e-001
+ 2X+: -9.44764e-002 -1.36856e-001
+ 2Y+: -1.04428e-001 5.27790e-003
+ 2Z+: 1.60710e-001 -7.74212e-002
+ 4X+: -9.17242e-002 -1.36656e-001
+ 4Y+: -1.34249e-001 -1.03884e-002
+ 4Z+: 1.92123e-001 -1.25627e-001
+ 5X+: 1.05875e-002 -1.03886e-001
+ 5Y+: -8.26338e-002 3.58498e-002
+ 5Z+: 2.55819e-001 -6.94290e-003
+ 6X+: -4.58970e-002 -1.33904e-002
+ 6Y+: -9.41660e-002 4.99682e-002
+ 6Z+: 1.28276e-001 4.59685e-002
+ 7X+: -6.01521e-002 -1.30165e-002
+ 7Y+: 2.56439e-003 -6.78141e-002
+ 7Z+: 5.03428e-002 -1.59420e-001
+ 8X+: -1.00895e-002 -8.80550e-002
+ 8Y+: 1.26327e-002 -8.14444e-002
+ 8Z+: 1.59506e-001 -2.05360e-001
+ 9X+: -3.04658e-003 -1.57921e-001
+ 9Y+: -8.23501e-002 4.82748e-002
+ 9Z+: 1.69315e-001 1.22804e-002
+ 10X+: -8.25875e-002 -7.31038e-002
+ 10Y+: -1.08668e-001 3.56364e-002
+ 10Z+: 8.28567e-002 -4.49596e-003
+ 11X+: -1.06792e-001 -6.95394e-002
+ 11Y+: 3.77195e-002 -7.65410e-002
+ 11Z+: 8.00590e-003 -2.32461e-002
+ 12X+: -4.84292e-002 -1.45790e-001
+ 12Y+: 1.03862e-002 -7.31212e-002
+ 12Z+: 1.78122e-001 -1.00939e-001
+ 13X+: -3.49891e-002 -6.20969e-003
+ 13Y+: -1.18504e-002 -1.94225e-002
+ 13Z+: 4.13007e-002 7.67087e-003
+ 14X+: -3.55795e-002 1.16708e-003
+ 14Y+: -1.68128e-002 -1.82344e-002
+ 14Z+: 3.92416e-002 -3.64434e-002
+ 15X+: -3.45304e-002 3.78185e-003
+ 15Y+: -7.62559e-003 -2.24241e-002
+ 15Z+: 6.28286e-003 -1.32711e-002
+ 16X+: -9.95646e-003 -6.04395e-003
+ 16Y+: -8.73465e-003 -2.20807e-002
+ 16Z+: 3.56946e-002 1.69231e-002
+ 17X+: -9.32661e-003 -5.51944e-003
+ 17Y+: -1.91087e-002 -9.09191e-003
+ 17Z+: 4.04981e-002 8.38685e-004
+ 18X+: -2.84456e-002 4.02762e-003
+ 18Y+: -2.20044e-002 -8.86197e-003
+ 18Z+: 4.43051e-002 -5.21033e-002
+ 19X+: -3.27019e-002 3.59765e-003
+ 19Y+: 2.93163e-003 -2.05064e-002
+ 19Z+: -1.77289e-002 -1.29477e-002
+ 20X+: -1.08474e-002 -5.78419e-003
+ 20Y+: 3.86759e-003 -1.91642e-002
+ 20Z+: 2.10135e-002 3.18051e-002
+ 3X+: -9.11657e-002 -1.36611e-001
+ 3Y+: -1.78165e-001 -3.47193e-002
+ 3Z+: 2.37121e-001 -4.96494e-002
+ 21X+: -1.34808e-002 -9.69121e-003
+ 21Y+: 1.25218e-002 -2.71411e-002
+ 21Z+: 2.76673e-001 0.00000e+000
+ 22X+: 1.96744e-003 4.90797e-003
+ 22Y+: -9.82609e-004 -3.31065e-002
+ 22Z+: 1.79246e-001 -3.33238e-002
+ 23X+: -1.08728e-002 -8.80278e-003
+ 23Z+: 2.30814e-001 -8.33151e-002
+ 23Y-: 1.15217e-002 4.01143e-002
+#+end_example
+
+#+begin_src matlab
+ mode4 = [...
+ -1.02501e-001-j*1.43802e-001, -1.07971e-001+j*5.61418e-004, +1.87145e-001-j*1.03605e-001;
+ -9.44764e-002-j*1.36856e-001, -1.04428e-001+j*5.27790e-003, +1.60710e-001-j*7.74212e-002;
+ -9.11657e-002-j*1.36611e-001, -1.78165e-001-j*3.47193e-002, +2.37121e-001-j*4.96494e-002;
+ -9.17242e-002-j*1.36656e-001, -1.34249e-001-j*1.03884e-002, +1.92123e-001-j*1.25627e-001;
+ +1.05875e-002-j*1.03886e-001, -8.26338e-002+j*3.58498e-002, +2.55819e-001-j*6.94290e-003;
+ -4.58970e-002-j*1.33904e-002, -9.41660e-002+j*4.99682e-002, +1.28276e-001+j*4.59685e-002;
+ -6.01521e-002-j*1.30165e-002, +2.56439e-003-j*6.78141e-002, +5.03428e-002-j*1.59420e-001;
+ -1.00895e-002-j*8.80550e-002, +1.26327e-002-j*8.14444e-002, +1.59506e-001-j*2.05360e-001;
+ -3.04658e-003-j*1.57921e-001, -8.23501e-002+j*4.82748e-002, +1.69315e-001+j*1.22804e-002;
+ -8.25875e-002-j*7.31038e-002, -1.08668e-001+j*3.56364e-002, +8.28567e-002-j*4.49596e-003;
+ -1.06792e-001-j*6.95394e-002, +3.77195e-002-j*7.65410e-002, +8.00590e-003-j*2.32461e-002;
+ -4.84292e-002-j*1.45790e-001, +1.03862e-002-j*7.31212e-002, +1.78122e-001-j*1.00939e-001;
+ -3.49891e-002-j*6.20969e-003, -1.18504e-002-j*1.94225e-002, +4.13007e-002+j*7.67087e-003;
+ -3.55795e-002+j*1.16708e-003, -1.68128e-002-j*1.82344e-002, +3.92416e-002-j*3.64434e-002;
+ -3.45304e-002+j*3.78185e-003, -7.62559e-003-j*2.24241e-002, +6.28286e-003-j*1.32711e-002;
+ -9.95646e-003-j*6.04395e-003, -8.73465e-003-j*2.20807e-002, +3.56946e-002+j*1.69231e-002;
+ -9.32661e-003-j*5.51944e-003, -1.91087e-002-j*9.09191e-003, +4.04981e-002+j*8.38685e-004;
+ -2.84456e-002+j*4.02762e-003, -2.20044e-002-j*8.86197e-003, +4.43051e-002-j*5.21033e-002;
+ -3.27019e-002+j*3.59765e-003, +2.93163e-003-j*2.05064e-002, -1.77289e-002-j*1.29477e-002;
+ -1.08474e-002-j*5.78419e-003, +3.86759e-003-j*1.91642e-002, +2.10135e-002+j*3.18051e-002;
+ -1.34808e-002-j*9.69121e-003, +1.25218e-002-j*2.71411e-002, +2.76673e-001+j*0.00000e+000;
+ +1.96744e-003+j*4.90797e-003, -9.82609e-004-j*3.31065e-002, +1.79246e-001-j*3.33238e-002;
+ -1.08728e-002-j*8.80278e-003, -1.15217e-002-j*4.01143e-002, +2.30814e-001-j*8.33151e-002];
+#+end_src
+
+*** All modes
+#+begin_src matlab
+mode_shapes = zeros(23, 3, 10);
+
+mode_shapes(:, :, 1) = [...
+-9.34637e-002+j*4.52445e-002, +2.33790e-001+j*1.41439e-003, -1.73754e-002+j*6.02449e-003;
+-7.42108e-002+j*3.91543e-002, +2.41566e-001-j*1.44869e-003, -5.99285e-003+j*2.10370e-003;
+-9.40720e-002+j*3.93724e-002, +2.52307e-001+j*0.00000e+000, -1.53864e-002-j*9.25720e-004;
+-1.02163e-001+j*2.79561e-002, +2.29048e-001+j*2.89782e-002, -2.85130e-002+j*1.77132e-004;
+-8.77132e-002+j*3.34081e-002, +2.14182e-001+j*2.14655e-002, -1.54521e-002+j*1.26682e-002;
+-7.90143e-002+j*2.42583e-002, +2.20669e-001+j*2.12738e-002, +4.60755e-002+j*4.96406e-003;
+-7.79654e-002+j*2.58385e-002, +2.06861e-001+j*3.48019e-002, -1.78311e-002-j*1.29704e-002;
+-8.49357e-002+j*3.55200e-002, +2.07470e-001+j*3.59745e-002, -7.66974e-002-j*3.19813e-003;
+-7.38565e-002+j*1.95146e-002, +2.17403e-001+j*2.01550e-002, -1.77073e-002-j*3.46414e-003;
+-7.77587e-002+j*2.36700e-002, +2.35654e-001-j*2.14540e-002, +7.94165e-002-j*2.45897e-002;
+-8.17972e-002+j*2.20583e-002, +2.20906e-001-j*4.30164e-003, -5.60520e-003+j*3.10187e-003;
+-8.64261e-002+j*3.66022e-002, +2.15000e-001-j*5.74661e-003, -1.22622e-001+j*4.11767e-002;
+-4.25169e-002+j*1.56602e-002, +5.31036e-002-j*1.73951e-002, -4.07130e-002+j*1.26884e-002;
+-3.85032e-002+j*1.29431e-002, +5.36716e-002-j*1.80868e-002, +1.00367e-001-j*3.48798e-002;
+-4.25524e-002+j*1.46363e-002, +5.19668e-002-j*1.69744e-002, +5.89747e-003-j*2.32428e-003;
+-4.31268e-002+j*1.38332e-002, +5.07545e-002-j*1.53045e-002, -1.04172e-001+j*3.17984e-002;
+-2.69757e-002+j*9.07955e-003, +3.07837e-002-j*9.44663e-003, -7.63502e-003+j*1.68203e-003;
+-3.00097e-002+j*9.23966e-003, +2.83585e-002-j*8.97747e-003, +1.52467e-001-j*4.78675e-002;
+-2.70223e-002+j*6.16478e-003, +3.06149e-002-j*6.25382e-003, -4.84888e-003+j*1.93970e-003;
+-2.90976e-002+j*7.13184e-003, +3.36738e-002-j*7.30875e-003, -1.66902e-001+j*3.93419e-002;
+-7.91940e-002+j*4.39648e-002, +2.04567e-001+j*9.49987e-003, -1.56087e-002+j*7.08838e-003;
+-1.01070e-001+j*3.13534e-002, +1.92270e-001+j*1.80423e-002, +2.93053e-003-j*1.97308e-003;
+-8.86455e-002+j*4.29906e-002, -3.38351e-002+j*1.81362e-003, +1.90862e-001+j*2.53414e-002];
+
+mode_shapes(:, :, 2) = [...
++7.56931e-002+j*3.61548e-002, +2.07574e-001+j*1.69205e-004, +1.29733e-002-j*6.78426e-004;
++8.58732e-002+j*2.54470e-002, +2.07117e-001-j*1.31755e-003, -2.13788e-003-j*1.24974e-002;
++8.17201e-002+j*2.36079e-002, +2.15927e-001+j*1.61300e-002, -5.48456e-004+j*2.55691e-002;
++7.09825e-002+j*3.66313e-002, +2.09969e-001+j*1.11484e-002, +9.19478e-003+j*3.47272e-002;
++6.23935e-002+j*1.02488e-002, +2.30687e-001-j*3.58416e-003, +3.27122e-002-j*5.85468e-002;
++7.61163e-002-j*2.43630e-002, +2.26743e-001-j*1.15334e-002, -6.20205e-003-j*1.21742e-001;
++8.01824e-002-j*1.94769e-002, +1.97485e-001+j*4.50105e-002, -2.21170e-002+j*9.77052e-002;
++6.19294e-002+j*8.15075e-003, +2.03864e-001+j*4.45835e-002, +2.55133e-002+j*1.36137e-001;
++4.38135e-002+j*7.30537e-002, +2.28426e-001-j*6.58868e-003, +1.16313e-002+j*5.09427e-004;
++5.45770e-002+j*4.34251e-002, +2.50823e-001+j*0.00000e+000, -4.63460e-002-j*4.76868e-002;
++5.50987e-002+j*4.26178e-002, +2.29394e-001+j*5.78236e-002, +1.90158e-002+j*1.09139e-002;
++4.98867e-002+j*7.30190e-002, +2.07871e-001+j*4.57750e-002, +6.69433e-002+j*9.00315e-002;
++2.48819e-002+j*3.03222e-002, -2.56046e-002-j*3.34132e-002, +2.13260e-002+j*2.58544e-002;
++2.45706e-002+j*2.60221e-002, -2.57723e-002-j*3.35612e-002, -5.71282e-002-j*6.61562e-002;
++2.68196e-002+j*2.83888e-002, -2.57263e-002-j*3.29627e-002, -2.11722e-003-j*3.37239e-003;
++2.51442e-002+j*3.32558e-002, -2.54372e-002-j*3.25062e-002, +5.65780e-002+j*7.64142e-002;
++1.62437e-002+j*1.94534e-002, -1.31293e-002-j*2.05924e-002, +1.05274e-003+j*3.59474e-003;
++1.83431e-002+j*2.03836e-002, -1.16818e-002-j*1.86334e-002, -8.66632e-002-j*1.08216e-001;
++1.62553e-002+j*1.79588e-002, -1.28857e-002-j*1.90512e-002, +6.25653e-003+j*4.97733e-003;
++1.63830e-002+j*2.03943e-002, -1.48941e-002-j*2.11717e-002, +8.68045e-002+j*1.16491e-001;
++6.79204e-002-j*5.55513e-002, +2.32871e-001+j*2.33389e-002, +1.34345e-002-j*2.31815e-002;
++4.02414e-002-j*8.38957e-002, +2.35273e-001+j*2.73256e-002, -8.51632e-003-j*7.49635e-003;
++6.18293e-002-j*5.99671e-002, +1.63533e-002+j*6.09161e-002, +2.37693e-001+j*4.34204e-002];
+
+mode_shapes(:, :, 3) = [...
++1.34688e-001-j*6.65071e-002, +1.55316e-002+j*1.01277e-002, -5.88466e-002+j*1.14294e-002;
++1.53934e-001-j*9.76990e-003, +7.17487e-003+j*1.11925e-002, -4.57205e-002+j*7.26573e-003;
++1.61551e-001+j*1.65478e-002, -4.12527e-004-j*5.60909e-002, -9.00640e-003+j*3.50754e-003;
++1.37298e-001-j*5.24661e-002, +1.19427e-003-j*5.39240e-002, -1.25915e-002+j*5.38133e-003;
++2.43192e-001-j*3.17374e-002, -2.15730e-001-j*7.69941e-004, -1.56268e-001+j*1.44118e-002;
+-7.27705e-002-j*3.54943e-003, -2.47706e-001+j*2.66480e-003, -1.21590e-001+j*1.06054e-002;
+-7.25870e-002-j*4.62024e-003, +2.27073e-001-j*3.69315e-002, +1.22611e-001-j*6.67337e-003;
++2.32731e-001-j*2.85516e-002, +2.35389e-001-j*3.81905e-002, +5.35574e-002+j*4.30394e-004;
++2.64170e-001-j*2.67367e-002, -2.56227e-001+j*3.97957e-005, -1.95398e-001+j*2.23549e-002;
+-1.66953e-002-j*7.95698e-003, -2.66547e-001-j*2.17687e-002, +1.56278e-002+j*2.23786e-003;
+-3.42364e-002-j*9.30205e-003, +2.52340e-001-j*7.47237e-003, -9.51643e-004+j*3.64798e-003;
++2.97574e-001+j*0.00000e+000, +2.23170e-001-j*1.37831e-002, +1.06266e-001+j*2.30324e-003;
++2.67178e-002-j*4.15723e-004, +6.75423e-003-j*2.18428e-003, -1.69423e-002+j*3.12395e-003;
+-1.12283e-002+j*2.86316e-004, +5.08225e-003-j*2.14053e-003, +2.18339e-002-j*3.25204e-003;
+-1.17948e-002+j*6.82873e-004, +1.94914e-002-j*2.42151e-003, +2.68660e-003-j*2.92104e-004;
++1.19490e-002+j*1.72236e-005, +1.83552e-002-j*2.71289e-003, -2.70914e-002+j*4.84164e-003;
++1.00173e-002-j*5.80552e-005, -3.87262e-003-j*1.19607e-003, -8.53809e-003+j*1.48424e-003;
+-1.22262e-002+j*5.13096e-004, -5.73905e-003-j*1.07659e-003, +3.51730e-002-j*6.13814e-003;
+-1.43735e-002-j*4.78552e-004, +2.31135e-002-j*6.30554e-004, +1.80171e-003-j*1.98835e-004;
++9.17792e-003+j*5.36661e-004, +2.18969e-002-j*5.81759e-004, -3.72117e-002+j*5.35813e-003;
++3.38754e-002-j*3.38703e-002, -2.20843e-002+j*2.78581e-002, -8.79541e-002-j*3.67473e-003;
++3.93064e-002+j*4.69476e-002, -1.69132e-002-j*1.04606e-002, -1.85351e-002+j*1.33750e-003;
++3.60396e-002-j*2.46238e-002, +3.57722e-003+j*3.64827e-003, -1.92038e-002-j*6.65895e-002];
+
+mode_shapes(:, :, 4) = [...
+-1.02501e-001-j*1.43802e-001, -1.07971e-001+j*5.61418e-004, +1.87145e-001-j*1.03605e-001;
+-9.44764e-002-j*1.36856e-001, -1.04428e-001+j*5.27790e-003, +1.60710e-001-j*7.74212e-002;
+-9.11657e-002-j*1.36611e-001, -1.78165e-001-j*3.47193e-002, +2.37121e-001-j*4.96494e-002;
+-9.17242e-002-j*1.36656e-001, -1.34249e-001-j*1.03884e-002, +1.92123e-001-j*1.25627e-001;
++1.05875e-002-j*1.03886e-001, -8.26338e-002+j*3.58498e-002, +2.55819e-001-j*6.94290e-003;
+-4.58970e-002-j*1.33904e-002, -9.41660e-002+j*4.99682e-002, +1.28276e-001+j*4.59685e-002;
+-6.01521e-002-j*1.30165e-002, +2.56439e-003-j*6.78141e-002, +5.03428e-002-j*1.59420e-001;
+-1.00895e-002-j*8.80550e-002, +1.26327e-002-j*8.14444e-002, +1.59506e-001-j*2.05360e-001;
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++3.26966e-002+j*1.03975e-002, -8.55682e-002-j*4.71847e-002, +3.99404e-002+j*8.59358e-003;
++3.45452e-002-j*3.05951e-003, -7.73823e-002-j*2.32199e-002, +2.30960e-002-j*7.49928e-003;
+-3.72461e-003-j*5.40336e-003, +1.80151e-001-j*1.42898e-002, -8.63921e-003+j*1.95638e-002;
+-1.11285e-002-j*2.22175e-003, +6.92355e-002-j*1.24144e-002, +8.02097e-002-j*6.81531e-003;
+-2.99885e-002-j*4.21951e-004, +8.19709e-002+j*1.22484e-002, +3.97531e-002+j*1.33874e-002;
+-1.59231e-002-j*3.96929e-003, +9.31295e-002+j*9.75532e-003, -4.01947e-002-j*5.17841e-003;
+-7.32828e-003-j*2.93496e-002, +4.39909e-002+j*1.25298e-002, -8.87525e-002+j*2.05359e-002;
++8.20167e-002+j*6.86693e-004, +4.25475e-001-j*2.36494e-002, +3.37034e-001-j*2.44199e-002;
+-2.68694e-002+j*3.82921e-003, +4.79292e-001+j*1.35903e-002, +5.06762e-001+j*0.00000e+000;
++1.40565e-002-j*5.41957e-003, +1.17563e-001+j*2.50398e-002, -5.97219e-002+j*5.92813e-004;
++2.30939e-002+j*1.16755e-002, +4.11136e-003+j*1.65726e-002, +2.41863e-002+j*5.06658e-002;
+-4.92960e-003+j*9.24082e-003, -5.44667e-003+j*1.41983e-002, -3.73537e-002-j*1.87263e-002;
++9.68682e-003+j*1.11791e-002, -5.13436e-003+j*1.29205e-002, -4.88765e-002-j*4.97821e-002;
+-1.66711e-003+j*1.03280e-002, +9.57955e-004+j*1.28350e-002, +3.30268e-002+j*5.44211e-002;
++5.90540e-003+j*1.67113e-002, +1.34280e-002+j*2.62111e-002, +4.38613e-002+j*7.17028e-002;
++4.97752e-003+j*1.47634e-002, +1.56773e-002+j*3.16026e-002, -5.27493e-002-j*3.38315e-002;
++2.83485e-003+j*1.14816e-002, +9.80676e-003+j*2.51504e-002, -6.78645e-002-j*9.90875e-002;
++5.62294e-003+j*1.84035e-002, +1.03717e-002+j*2.37801e-002, +2.58497e-002+j*3.75352e-002;
+-8.75236e-003-j*4.71723e-003, +6.99107e-002+j*1.51894e-002, +3.46273e-002+j*1.48547e-002;
+-1.72822e-002-j*8.75192e-003, +6.96759e-002+j*1.59783e-002, +8.07917e-002+j*1.97809e-002;
+-1.29601e-002-j*5.61834e-003, +1.76126e-002+j*4.62761e-003, +6.64667e-002+j*1.61199e-002];
+#+end_src
+
+** Define a point for each solid body
+We define accelerometer indices used to define the motion of each solid body (2 3-axis accelerometer are enough).
+#+begin_src matlab
+ stages = [17, 19; % Bottom Granite
+ 13, 15; % Top Granite
+ 9, 11; % Ty
+ 5, 7; % Ry
+ 21, 22; % Spindle
+ 1, 3]; % Hexapod
+#+end_src
+
+We define the origin point ${}^AO_B$ of the solid body $\{B\}$.
+Here we choose the middle point between the two accelerometers.
+This could be define differently (for instance by choosing the center of mass).
+#+begin_src matlab
+ AOB = zeros(3, size(stages, 1));
+
+ for i = 1:size(stages, 1)
+ AOB(:, i) = mean(positions(stages(i, :), 1:3))';
+ end
+#+end_src
+
+Then we compute the positions of the sensors with respect to the previously defined origin for the frame $\{B\}$: ${}^BP_1$ and ${}^BP_2$.
+#+begin_src matlab
+ BP1 = zeros(3, size(stages, 1));
+ BP2 = zeros(3, size(stages, 1));
+
+ for i = 1:size(stages, 1)
+ BP1(:, i) = positions(stages(i, 1), 1:3)' - AOB(:, i);
+ BP2(:, i) = positions(stages(i, 2), 1:3)' - AOB(:, i);
+ end
+#+end_src
+
+Let's define one absolute frame $\{A\}$ and one frame $\{B\}$ fixed w.r.t. the solid body.
+We note ${}^AO_B$ the position of origin of $\{B\}$ expressed in $\{A\}$.
+
+We are measuring with the accelerometers the absolute motion of points $P_1$ and $P_2$: ${}^Av_{P_1}$ and ${}^Av_{P_2}$.
+
+Let's note ${}^BP_1$ and ${}^BP_2$ the (known) coordinates of $P_1$ and $P_2$ expressed in the frame $\{B\}$.
+
+Then we have:
+\begin{align}
+ {}^Av_{P_1} &= {}^Av_{O_B} + {}^A\Omega^\times {}^AR_B {}^BP_1 \\
+ {}^Av_{P_2} &= {}^Av_{O_B} + {}^A\Omega^\times {}^AR_B {}^BP_2
+\end{align}
+
+And we obtain
+\begin{align}
+ {}^A\Omega^\times {}^AR_B &= \left( {}^Av_{P_2} - {}^Av_{P_1} \right) \left( {}^BP_2 - {}^BP_1 \right)^{-1}\\
+ {}^Av_{O_B} &= {}^Av_{P_1} - \left( {}^Av_{P_2} - {}^Av_{P_1} \right) \left( {}^BP_2 - {}^BP_1 \right)^{-1} {}^BP_1
+\end{align}
+
+#+begin_src matlab
+ AVOB = zeros(3, size(stages, 1));
+ ARB = zeros(3, 3, size(stages, 1));
+ for i = 1:size(stages, 1)
+ AVOB(:, i) = mode1(stages(i, 1), :)' - (mode1(stages(i, 2), :)' - mode1(stages(i, 1), :)')*pinv(BP2(:, i) - BP1(:, i))*BP1(:, i);
+ ARB(:, :, i) = (mode1(stages(i, 2), :)' - mode1(stages(i, 1), :)')*pinv(BP2(:, i) - BP1(:, i));
+ end
+#+end_src
+
+** Argand Diagram
+For mode 1
+
+#+begin_src matlab
+ figure;
+ hold on;
+ for i=1:size(mode1, 1)
+ plot([0, real(mode1(i, 1))], [0, imag(mode1(i, 1))], '-k')
+ plot([0, real(mode1(i, 2))], [0, imag(mode1(i, 2))], '-k')
+ plot([0, real(mode1(i, 3))], [0, imag(mode1(i, 3))], '-k')
+
+ % plot([0, real(mode2(i, 1))], [0, imag(mode2(i, 1))], '-r')
+ % plot([0, real(mode2(i, 2))], [0, imag(mode2(i, 2))], '-r')
+ % plot([0, real(mode2(i, 3))], [0, imag(mode2(i, 3))], '-r')
+
+ % plot([0, real(mode3(i, 1))], [0, imag(mode3(i, 1))], '-b')
+ % plot([0, real(mode3(i, 2))], [0, imag(mode3(i, 2))], '-b')
+ % plot([0, real(mode3(i, 3))], [0, imag(mode3(i, 3))], '-b')
+ end
+
+ for i=1:size(AVOB, 2)
+ plot([0, real(AVOB(1, i))], [0, imag(AVOB(1, i))], '-r')
+ plot([0, real(AVOB(2, i))], [0, imag(AVOB(2, i))], '-r')
+ plot([0, real(AVOB(3, i))], [0, imag(AVOB(3, i))], '-r')
+ end
+
+ % ang=0:0.01:2*pi;
+ % radius1 = max(max(sqrt(real(mode1).^2+imag(mode1).^2)));
+ % plot(radius1*cos(ang), radius1*sin(ang), '-k');
+
+ % radius2 = max(max(sqrt(real(mode2).^2+imag(mode2).^2)));
+ % plot(radius2*cos(ang), radius2*sin(ang), '-r');
+
+ % radius3 = max(max(sqrt(real(mode3).^2+imag(mode3).^2)));
+ % plot(radius3*cos(ang), radius3*sin(ang), '-b');
+
+ hold off;
+ axis manual equal
+#+end_src
+
+** TEST: animate first mode
+#+begin_src matlab
+ figure;
+ hold on;
+ fill3(positions(1:4, 1), positions(1:4, 2), positions(1:4, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(5:8, 1), positions(5:8, 2), positions(5:8, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(9:12, 1), positions(9:12, 2), positions(9:12, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(13:16, 1), positions(13:16, 2), positions(13:16, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(17:20, 1), positions(17:20, 2), positions(17:20, 3), 'k', 'FaceAlpha', 0.5)
+ fill3(positions(21:23, 1), positions(21:23, 2), positions(21:23, 3), 'k', 'FaceAlpha', 0.5)
+ hold off;
+#+end_src
+
+#+NAME: fig:mode_shapes
+#+HEADER: :tangle no :exports results :results value file raw replace :noweb yes
+#+begin_src matlab
+ rec = polyshape([-2 -2 2 2],[-3 3 3 -3]);
+ h = figure;
+ filename = 'figs/mode_shapes.gif';
+ n = 20;
+
+ for i = 1:n
+ axis manual equal
+
+ Dm = real(V(1:3, 5)*cos(2*pi*i/n));
+ rec_i = rotate(rec, 180/pi*Dm(3));
+ rec_i = translate(rec_i, 10*Dm(1), 10*Dm(2));
+ plot(rec_i);
+
+ xlim([-3, 3]); ylim([-4, 4]);
+
+ set(h, 'visible', 'off');
+ set(h, 'pos', [0, 0, 500, 500]);
+ drawnow;
+
+ % Capture the plot as an image
+ frame = getframe(h);
+ im = frame2im(frame);
+ [imind,cm] = rgb2ind(im,256);
+
+ % Write to the GIF File
+ if i == 1
+ imwrite(imind,cm,filename,'gif','DelayTime',0.1,'Loopcount',inf);
+ else
+ imwrite(imind,cm,filename,'gif','DelayTime',0.1,'WriteMode','append');
+ end
+ end
+
+ set(h, 'visible', 'on');
+ ans = filename;
+#+end_src
+
+** From 6 translations to translation + rotation
+Let's define one absolute frame $\{A\}$ and one frame $\{B\}$ fixed w.r.t. the solid body.
+We note ${}^AO_B$ the position of origin of $\{B\}$ expressed in $\{A\}$.
+
+We are measuring with the accelerometers the absolute motion of points $P_1$ and $P_2$: ${}^AP_1$ and ${}^AP_2$.
+
+Let's note ${}^BP_1$ and ${}^BP_2$ the (known) coordinates of $P_1$ and $P_2$ expressed in the frame $\{B\}$.
+
+Then we have:
+\begin{align}
+ {}^AP_1 &= {}^AO_B + {}^AR_B {}^BP_1 \\
+ {}^AP_2 &= {}^AO_B + {}^AR_B {}^BP_2
+\end{align}
+
+And we obtain
+\begin{align}
+ {}^AR_B &= \left( {}^AP_2 - {}^AP_1 \right) \left( {}^BP_2 - {}^BP_1 \right)^{-1}\\
+ {}^AO_B &= {}^Av_{P_1} - \left( {}^AP_2 - {}^AP_1 \right) \left( {}^BP_2 - {}^BP_1 \right)^{-1} {}^BP_1
+\end{align}
+
+* Problem with AirLoc System
+The mode shape of the first mode at 11Hz (figure [[fig:mode1]]) seems to indicate that this corresponds to a suspension mode.
+
+This could be due to the 4 Airloc Levelers that are used for the granite (figure [[fig:airloc]]).
+
+#+name: fig:airloc
+#+caption: AirLoc used for the granite (2120-KSKC)
+#+attr_html: :width 500px
+[[file:img/airloc/IMG_20190618_155522.jpg]]
+
+They are probably *not well leveled*, so the granite is supported only by two Airloc.
+
+
* Setup
#+name: fig:nass-modal-test
#+caption: Position and orientation of the accelerometer used
@@ -516,7 +1670,7 @@ For each measurement file, the FRF and coherence between the impact and the 9 ac
In reality: 4 sets of 10 things
#+begin_src matlab
- a = load('./modal_analysis/frf_coh/Measurement1.mat');
+ a = load('mat/meas_frf_coh_1.mat');
#+end_src
#+begin_src matlab
@@ -574,7 +1728,7 @@ FRF matrix $n \times p$:
% Loop through measurements
for i = 1:n_meas
% Load the measurement file
- meas = load(sprintf('./modal_analysis/frf_coh/Measurement%i.mat', i));
+ meas = load(sprintf('mat/meas_frf_coh_%i.mat', i));
% First: determine what is the exitation (direction and sign)
exc_dir = meas.FFT1_AvXSpc_2_1_RMS_RfName(end);
@@ -822,6 +1976,9 @@ From the computed FRF of the Hexapod in its 6 DOFs, compute the FRF of the accel
#+begin_important
The reduction of the number of degrees of freedom from 69 (23 accelerometers with each 3DOF) to 36 (6 solid bodies with 6 DOF) seems to work well.
+
+ This confirms the fact that this stage, for that mode is indeed behaving as a solid body.
+ This should be verified for all the stages for modes with high resonance frequencies.
#+end_important
* TODO Synthesis of FRF curves