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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-06-19 mer. 10:38 -->
<!-- 2019-06-19 mer. 11:14 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Modal Analysis</title>
@ -280,50 +280,55 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgac37ea1">1. Goal</a></li>
<li><a href="#org2c806fc">2. Type of Model</a></li>
<li><a href="#orgc645667">3. Instrumentation Used</a></li>
<li><a href="#org1a9bf2b">4. Structure Preparation and Test Planning</a>
<li><a href="#org1d79a68">1. Goal</a></li>
<li><a href="#orgde6e655">2. Type of Model</a></li>
<li><a href="#org9414b8d">3. Instrumentation Used</a></li>
<li><a href="#org521ef27">4. Structure Preparation and Test Planning</a>
<ul>
<li><a href="#orgec92624">4.1. Structure Preparation</a></li>
<li><a href="#orgf3e7d52">4.2. Test Planing</a></li>
<li><a href="#orge605474">4.3. Location of the Accelerometers</a></li>
<li><a href="#org9371de2">4.4. Hammer Impacts</a></li>
<li><a href="#orga7b6b16">4.1. Structure Preparation</a></li>
<li><a href="#org62eba0c">4.2. Test Planing</a></li>
<li><a href="#org9c54744">4.3. Location of the Accelerometers</a></li>
<li><a href="#org2ba755b">4.4. Hammer Impacts</a></li>
</ul>
</li>
<li><a href="#orgc76dac6">5. Measurements</a>
<li><a href="#org9bef537">5. Signal Processing</a></li>
<li><a href="#org857fbe9">6. Frequency Response Functions and Coherence Results</a>
<ul>
<li><a href="#org1409591">5.1. Signal Processing</a></li>
<li><a href="#org32f97d8">6.1. Load Data</a></li>
<li><a href="#orgf4cdb9c">6.2. Raw Force Data</a></li>
<li><a href="#org8a25453">6.3. Raw Response Data</a></li>
<li><a href="#org7c2ca7a">6.4. Load Data</a></li>
<li><a href="#org21b3b6b">6.5. FRF and Coherence Results</a></li>
</ul>
</li>
<li><a href="#orga28022b">6. FRF and COH Results</a></li>
<li><a href="#orgd5a7271">7. Mode Shapes</a></li>
<li><a href="#org56702cf">8. Problem with AirLoc System</a></li>
<li><a href="#orgf013fb5">9. Spatial Mode Extraction</a></li>
<li><a href="#org01620a5">7. Mode Shapes</a></li>
<li><a href="#org7403c04">8. Obtained Modal Matrices</a></li>
<li><a href="#orge615fec">9. Problem with AirLoc System</a></li>
<li><a href="#orge98bc94">10. Spatial Mode Extraction</a></li>
</ul>
</div>
</div>
<div id="outline-container-orgac37ea1" class="outline-2">
<h2 id="orgac37ea1"><span class="section-number-2">1</span> Goal</h2>
<div id="outline-container-org1d79a68" class="outline-2">
<h2 id="org1d79a68"><span class="section-number-2">1</span> Goal</h2>
<div class="outline-text-2" id="text-1">
<p>
The goal is to experimentally extract a <b>Spatial Model</b> (mass, damping, stiffness) of the structure (shown on figure <a href="#orgbd596be">1</a>) in order to tune the Multi-Body model.
The goal is to experimentally extract a <b>Spatial Model</b> (mass, damping, stiffness) of the structure (shown on figure <a href="#org554eed5">1</a>) in order to tune the Multi-Body model.
</p>
<div id="orgbd596be" class="figure">
<div id="org554eed5" class="figure">
<p><img src="img/nass_picture.png" alt="nass_picture.png" width="500px" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass</p>
</div>
<p>
The procedure is represented on figure <a href="#orge0db9c5">2</a> where we go from left to right.
The procedure is represented on figure <a href="#orgee4af11">2</a> where we go from left to right.
</p>
<div id="orge0db9c5" class="figure">
<div id="orgee4af11" class="figure">
<p><img src="img/vibration_analysis_procedure.png" alt="vibration_analysis_procedure.png" width="400px" />
</p>
<p><span class="figure-number">Figure 2: </span>Vibration Analysis Procedure</p>
@ -346,13 +351,13 @@ The modes we want to identify are those in the frequency range between 0Hz and 1
</div>
</div>
<div id="outline-container-org2c806fc" class="outline-2">
<h2 id="org2c806fc"><span class="section-number-2">2</span> Type of Model</h2>
<div id="outline-container-orgde6e655" class="outline-2">
<h2 id="orgde6e655"><span class="section-number-2">2</span> Type of Model</h2>
<div class="outline-text-2" id="text-2">
<p>
The model that we want to obtain is a <b>multi-body model</b>.
It is composed of several <b>solid bodies connected with springs and dampers</b>.
The solid bodies are represented with different colors on figure <a href="#org6bc27d8">3</a>.
The solid bodies are represented with different colors on figure <a href="#org15f16cb">3</a>.
</p>
<p>
@ -367,7 +372,7 @@ In the simscape model, the solid bodies are:
</ul>
<div id="org6bc27d8" class="figure">
<div id="org15f16cb" class="figure">
<p><img src="img/nass_solidworks.png" alt="nass_solidworks.png" width="800px" />
</p>
<p><span class="figure-number">Figure 3: </span>CAD view of the ID31 Micro-Station</p>
@ -384,20 +389,20 @@ The modal identification done here will thus permit us to determine <b>which DOF
</div>
</div>
<div id="outline-container-orgc645667" class="outline-2">
<h2 id="orgc645667"><span class="section-number-2">3</span> Instrumentation Used</h2>
<div id="outline-container-org9414b8d" class="outline-2">
<h2 id="org9414b8d"><span class="section-number-2">3</span> Instrumentation Used</h2>
<div class="outline-text-2" id="text-3">
<p>
In order to perform to Modal Analysis and to obtain first a Response Model, the following devices are used:
</p>
<ul class="org-ul">
<li>An <b>acquisition system</b> (OROS) with 24bits ADCs (figure <a href="#orga72e510">4</a>)</li>
<li>3 tri-axis <b>Accelerometers</b> (figure <a href="#orge04521f">5</a>) with parameters shown on table <a href="#org69d60d7">1</a></li>
<li>An <b>Instrumented Hammer</b> with various Tips (figure <a href="#org809d290">6</a>) (figure <a href="#org0fe6440">7</a>)</li>
<li>An <b>acquisition system</b> (OROS) with 24bits ADCs (figure <a href="#org754b9bb">4</a>)</li>
<li>3 tri-axis <b>Accelerometers</b> (figure <a href="#org60ed8da">5</a>) with parameters shown on table <a href="#org3ef74f2">1</a></li>
<li>An <b>Instrumented Hammer</b> with various Tips (figure <a href="#org4dfa916">6</a>) (figure <a href="#orgeffae9f">7</a>)</li>
</ul>
<div id="orga72e510" class="figure">
<div id="org754b9bb" class="figure">
<p><img src="img/instrumentation/oros.png" alt="oros.png" width="500px" />
</p>
<p><span class="figure-number">Figure 4: </span>Acquisition system: OROS</p>
@ -410,13 +415,13 @@ Anti-aliasing filters are also included in the system.
</p>
<div id="orge04521f" class="figure">
<div id="org60ed8da" class="figure">
<p><img src="img/instrumentation/accelero_M393B05.png" alt="accelero_M393B05.png" width="500px" />
</p>
<p><span class="figure-number">Figure 5: </span>Accelerometer used: M393B05</p>
</div>
<table id="org69d60d7" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org3ef74f2" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> 393B05 Accelerometer Data Sheet</caption>
<colgroup>
@ -459,14 +464,14 @@ It excites more the low frequency range where the coherence is low, the overall
</p>
<div id="org809d290" class="figure">
<div id="org4dfa916" class="figure">
<p><img src="img/instrumentation/instrumented_hammer.png" alt="instrumented_hammer.png" width="500px" />
</p>
<p><span class="figure-number">Figure 6: </span>Instrumented Hammer</p>
</div>
<div id="org0fe6440" class="figure">
<div id="orgeffae9f" class="figure">
<p><img src="img/instrumentation/hammer_tips.png" alt="hammer_tips.png" width="500px" />
</p>
<p><span class="figure-number">Figure 7: </span>Hammer tips</p>
@ -478,12 +483,12 @@ The accelerometers are glued on the structure.
</div>
</div>
<div id="outline-container-org1a9bf2b" class="outline-2">
<h2 id="org1a9bf2b"><span class="section-number-2">4</span> Structure Preparation and Test Planning</h2>
<div id="outline-container-org521ef27" class="outline-2">
<h2 id="org521ef27"><span class="section-number-2">4</span> Structure Preparation and Test Planning</h2>
<div class="outline-text-2" id="text-4">
</div>
<div id="outline-container-orgec92624" class="outline-3">
<h3 id="orgec92624"><span class="section-number-3">4.1</span> Structure Preparation</h3>
<div id="outline-container-orga7b6b16" class="outline-3">
<h3 id="orga7b6b16"><span class="section-number-3">4.1</span> Structure Preparation</h3>
<div class="outline-text-3" id="text-4-1">
<p>
All the stages are turned ON.
@ -526,8 +531,8 @@ All other elements have been remove from the granite such as another heavy posit
</div>
</div>
<div id="outline-container-orgf3e7d52" class="outline-3">
<h3 id="orgf3e7d52"><span class="section-number-3">4.2</span> Test Planing</h3>
<div id="outline-container-org62eba0c" class="outline-3">
<h3 id="org62eba0c"><span class="section-number-3">4.2</span> Test Planing</h3>
<div class="outline-text-3" id="text-4-2">
<p>
The goal is to identify the full \(N \times N\) FRF matrix (where \(N\) is the number of degree of freedom of the system).
@ -560,8 +565,8 @@ The measurement thus consists of:
</div>
</div>
<div id="outline-container-orge605474" class="outline-3">
<h3 id="orge605474"><span class="section-number-3">4.3</span> Location of the Accelerometers</h3>
<div id="outline-container-org9c54744" class="outline-3">
<h3 id="org9c54744"><span class="section-number-3">4.3</span> Location of the Accelerometers</h3>
<div class="outline-text-3" id="text-4-3">
<p>
4 tri-axis accelerometers are used for each solid body.
@ -580,29 +585,29 @@ The position of the accelerometers are:
</p>
<ul class="org-ul">
<li>4 on the first granite</li>
<li>4 on the second granite (figure <a href="#orgf735e72">8</a>)</li>
<li>4 on top of the translation stage (figure <a href="#org9df7efa">9</a>)</li>
<li>4 on the second granite (figure <a href="#org40cad46">8</a>)</li>
<li>4 on top of the translation stage (figure <a href="#org48c6c2d">9</a>)</li>
<li>4 on top of the tilt stage</li>
<li>4 on top of the spindle</li>
<li>4 on top of the hexapod (figure <a href="#org33696af">10</a>)</li>
<li>4 on top of the hexapod (figure <a href="#org8e536a4">10</a>)</li>
</ul>
<div id="orgf735e72" class="figure">
<div id="org40cad46" class="figure">
<p><img src="img/accelerometers/accelerometers_granite2_overview.jpg" alt="accelerometers_granite2_overview.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 8: </span>Accelerometers located on the top granite</p>
</div>
<div id="org9df7efa" class="figure">
<div id="org48c6c2d" class="figure">
<p><img src="img/accelerometers/accelerometers_ty_overview.jpg" alt="accelerometers_ty_overview.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 9: </span>Accelerometers located on top of the translation stage</p>
</div>
<div id="org33696af" class="figure">
<div id="org8e536a4" class="figure">
<p><img src="img/accelerometers/accelerometers_hexa_overview.jpg" alt="accelerometers_hexa_overview.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 10: </span>Accelerometers located on the Hexapod</p>
@ -610,33 +615,33 @@ The position of the accelerometers are:
</div>
</div>
<div id="outline-container-org9371de2" class="outline-3">
<h3 id="org9371de2"><span class="section-number-3">4.4</span> Hammer Impacts</h3>
<div id="outline-container-org2ba755b" class="outline-3">
<h3 id="org2ba755b"><span class="section-number-3">4.4</span> Hammer Impacts</h3>
<div class="outline-text-3" id="text-4-4">
<p>
Only 3 impact points are used.
</p>
<p>
The impact points are shown on figures <a href="#orgbc6af07">11</a>, <a href="#orgcc517fd">12</a> and <a href="#orgdbdddee">13</a>.
The impact points are shown on figures <a href="#orgda6fe26">11</a>, <a href="#org5c809cf">12</a> and <a href="#org225af9b">13</a>.
</p>
<div id="orgbc6af07" class="figure">
<div id="orgda6fe26" class="figure">
<p><img src="img/impacts/hammer_x.gif" alt="hammer_x.gif" width="300px" />
</p>
<p><span class="figure-number">Figure 11: </span>Hammer Blow in the X direction</p>
</div>
<div id="orgcc517fd" class="figure">
<div id="org5c809cf" class="figure">
<p><img src="img/impacts/hammer_y.gif" alt="hammer_y.gif" width="300px" />
</p>
<p><span class="figure-number">Figure 12: </span>Hammer Blow in the Y direction</p>
</div>
<div id="orgdbdddee" class="figure">
<div id="org225af9b" class="figure">
<p><img src="img/impacts/hammer_z.gif" alt="hammer_z.gif" width="300px" />
</p>
<p><span class="figure-number">Figure 13: </span>Hammer Blow in the Z direction</p>
@ -645,19 +650,15 @@ The impact points are shown on figures <a href="#orgbc6af07">11</a>, <a href="#o
</div>
</div>
<div id="outline-container-orgc76dac6" class="outline-2">
<h2 id="orgc76dac6"><span class="section-number-2">5</span> Measurements</h2>
<div id="outline-container-org9bef537" class="outline-2">
<h2 id="org9bef537"><span class="section-number-2">5</span> Signal Processing</h2>
<div class="outline-text-2" id="text-5">
</div>
<div id="outline-container-org1409591" class="outline-3">
<h3 id="org1409591"><span class="section-number-3">5.1</span> Signal Processing</h3>
<div class="outline-text-3" id="text-5-1">
<p>
The measurements are averaged 10 times (figure <a href="#orga5a95f4">14</a>) corresponding to 10 hammer impacts.
The measurements are averaged 10 times (figure <a href="#orge55de2d">14</a>) corresponding to 10 hammer impacts.
</p>
<div id="orga5a95f4" class="figure">
<div id="orge55de2d" class="figure">
<p><img src="img/parameters/general_parameters.jpg" alt="general_parameters.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 14: </span>General Acquisition Settings</p>
@ -668,136 +669,327 @@ Windowing is used on the force response signals.
</p>
<p>
A boxcar window (figure <a href="#orgc036c52">15</a>) is used for the force signal as once the impact on the structure is done, the measured signal is meaningless.
A boxcar window (figure <a href="#orgd266960">15</a>) is used for the force signal as once the impact on the structure is done, the measured signal is meaningless.
</p>
<p>
An exponential window (figure <a href="#org90aa820">16</a>) 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.
An exponential window (figure <a href="#orgea90be6">16</a>) 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.
</p>
<div id="orgc036c52" class="figure">
<div id="orgd266960" class="figure">
<p><img src="img/parameters/window_force.jpg" alt="window_force.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 15: </span>Window used for the force signal</p>
</div>
<div id="org90aa820" class="figure">
<div id="orgea90be6" class="figure">
<p><img src="img/parameters/window_response.jpg" alt="window_response.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 16: </span>Window used for the response signal</p>
</div>
</div>
</div>
<div id="outline-container-org857fbe9" class="outline-2">
<h2 id="org857fbe9"><span class="section-number-2">6</span> Frequency Response Functions and Coherence Results</h2>
<div class="outline-text-2" id="text-6">
</div>
<div id="outline-container-org32f97d8" class="outline-3">
<h3 id="org32f97d8"><span class="section-number-3">6.1</span> Load Data</h3>
<div class="outline-text-3" id="text-6-1">
<div class="org-src-container">
<pre class="src src-matlab">meas1_raw = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'modal_analysis/raw_data/Measurement1.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orga28022b" class="outline-2">
<h2 id="orga28022b"><span class="section-number-2">6</span> FRF and COH Results</h2>
<div id="outline-container-orgf4cdb9c" class="outline-3">
<h3 id="orgf4cdb9c"><span class="section-number-3">6.2</span> Raw Force Data</h3>
<div class="outline-text-3" id="text-6-2">
<div id="org57be466" class="figure">
<p><img src="figs/raw_data_force.png" alt="raw_data_force.png" />
</p>
<p><span class="figure-number">Figure 17: </span>Raw Force Data from Hammer Blow</p>
</div>
<div id="outline-container-orgd5a7271" class="outline-2">
<h2 id="orgd5a7271"><span class="section-number-2">7</span> Mode Shapes</h2>
<div id="orgbfddb0e" class="figure">
<p><img src="figs/raw_data_foce_zoom.png" alt="raw_data_foce_zoom.png" />
</p>
<p><span class="figure-number">Figure 18: </span>Raw Force Data from Hammer Blow - Zoom</p>
</div>
</div>
</div>
<div id="outline-container-org8a25453" class="outline-3">
<h3 id="org8a25453"><span class="section-number-3">6.3</span> Raw Response Data</h3>
<div class="outline-text-3" id="text-6-3">
<div id="orga662a1c" class="figure">
<p><img src="figs/raw_data_acceleration.png" alt="raw_data_acceleration.png" />
</p>
<p><span class="figure-number">Figure 19: </span>Raw Acceleration Data from Accelerometer</p>
</div>
<div id="org1b7a108" class="figure">
<p><img src="figs/raw_data_acceleration_zoom.png" alt="raw_data_acceleration_zoom.png" />
</p>
<p><span class="figure-number">Figure 20: </span>Raw Acceleration Data from Accelerometer - Zoom</p>
</div>
</div>
</div>
<div id="outline-container-org7c2ca7a" class="outline-3">
<h3 id="org7c2ca7a"><span class="section-number-3">6.4</span> Load Data</h3>
<div class="outline-text-3" id="text-6-4">
<div class="org-src-container">
<pre class="src src-matlab">meas1 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'modal_analysis/frf_coh/Measurement1.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org21b3b6b" class="outline-3">
<h3 id="org21b3b6b"><span class="section-number-3">6.5</span> FRF and Coherence Results</h3>
<div class="outline-text-3" id="text-6-5">
<div id="orge9d2826" class="figure">
<p><img src="figs/frf_result_example.png" alt="frf_result_example.png" />
</p>
<p><span class="figure-number">Figure 21: </span>Example of one measured FRF</p>
</div>
<div id="orgfae7d9a" class="figure">
<p><img src="figs/coh_result_example.png" alt="coh_result_example.png" />
</p>
<p><span class="figure-number">Figure 22: </span>Example of one measured Coherence</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org01620a5" class="outline-2">
<h2 id="org01620a5"><span class="section-number-2">7</span> Mode Shapes</h2>
<div class="outline-text-2" id="text-7">
<p>
Multiple modal extraction techniques can be used (SIMO, MIMO, narrow band, wide band, &#x2026;).
First preliminary results on 10 identified modes are presented here.
</p>
<div id="orgd8ff148" class="figure">
<div id="orgaa57efe" class="figure">
<p><img src="img/modes/mode1.gif" alt="mode1.gif" />
</p>
<p><span class="figure-number">Figure 17: </span>Mode 1</p>
<p><span class="figure-number">Figure 23: </span>Mode 1</p>
</div>
<div id="org8d04700" class="figure">
<div id="org67a662e" class="figure">
<p><img src="img/modes/mode2.gif" alt="mode2.gif" />
</p>
<p><span class="figure-number">Figure 18: </span>Mode 2</p>
<p><span class="figure-number">Figure 24: </span>Mode 2</p>
</div>
<div id="orgf6bbcc2" class="figure">
<div id="org442b3c1" class="figure">
<p><img src="img/modes/mode3.gif" alt="mode3.gif" />
</p>
<p><span class="figure-number">Figure 19: </span>Mode 3</p>
<p><span class="figure-number">Figure 25: </span>Mode 3</p>
</div>
<div id="org65681ff" class="figure">
<div id="org874bdc2" class="figure">
<p><img src="img/modes/mode4.gif" alt="mode4.gif" />
</p>
<p><span class="figure-number">Figure 20: </span>Mode 4</p>
<p><span class="figure-number">Figure 26: </span>Mode 4</p>
</div>
<div id="orgf9a0639" class="figure">
<div id="org17b0003" class="figure">
<p><img src="img/modes/mode5.gif" alt="mode5.gif" />
</p>
<p><span class="figure-number">Figure 21: </span>Mode 5</p>
<p><span class="figure-number">Figure 27: </span>Mode 5</p>
</div>
<div id="org368c756" class="figure">
<div id="orge792930" class="figure">
<p><img src="img/modes/mode6.gif" alt="mode6.gif" />
</p>
<p><span class="figure-number">Figure 22: </span>Mode 6</p>
<p><span class="figure-number">Figure 28: </span>Mode 6</p>
</div>
<div id="org0664fec" class="figure">
<div id="org51bf469" class="figure">
<p><img src="img/modes/mode7.gif" alt="mode7.gif" />
</p>
<p><span class="figure-number">Figure 23: </span>Mode 7</p>
<p><span class="figure-number">Figure 29: </span>Mode 7</p>
</div>
<div id="org65c79b2" class="figure">
<div id="orgbbbf537" class="figure">
<p><img src="img/modes/mode8.gif" alt="mode8.gif" />
</p>
<p><span class="figure-number">Figure 24: </span>Mode 8</p>
<p><span class="figure-number">Figure 30: </span>Mode 8</p>
</div>
<div id="org261f452" class="figure">
<div id="orgda7c6b4" class="figure">
<p><img src="img/modes/mode9.gif" alt="mode9.gif" />
</p>
<p><span class="figure-number">Figure 25: </span>Mode 9</p>
<p><span class="figure-number">Figure 31: </span>Mode 9</p>
</div>
<div id="org4881e36" class="figure">
<div id="org3deb93b" class="figure">
<p><img src="img/modes/mode10.gif" alt="mode10.gif" />
</p>
<p><span class="figure-number">Figure 26: </span>Mode 10</p>
<p><span class="figure-number">Figure 32: </span>Mode 10</p>
</div>
</div>
</div>
<div id="outline-container-org56702cf" class="outline-2">
<h2 id="org56702cf"><span class="section-number-2">8</span> Problem with AirLoc System</h2>
<div id="outline-container-org7403c04" class="outline-2">
<h2 id="org7403c04"><span class="section-number-2">8</span> Obtained Modal Matrices</h2>
<div class="outline-text-2" id="text-8">
<p>
4 Airloc Levelers are used for the granite (figure <a href="#org6ddfc9a">27</a>).
From the modal analysis software, we can export the obtained <b>eigen matrices</b>:
\[ \begin{bmatrix}
\omega_1^2 & & 0 \\
& \ddots & \\
0 & & \omega_n^2
\end{bmatrix}; \quad \Psi = \begin{bmatrix}
& & \\
\{\psi_1\} & \dots & \{\psi_n\} \\
& &
\end{bmatrix} \]
</p>
<p>
where \(\bar{\omega}_r^2\) is the \(r^\text{th}\) eigenvalue squared and \(\{\phi\}_r\) is a description of the corresponding <b>mode shape</b>.
</p>
<p>
The file containing the eigen frequencies and mode shapes are shown below (for the first mode).
</p>
<pre class="example">
Created by N-Modal
Estimator: cmif
18-Jun-19 16:31:25
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
</pre>
</div>
</div>
<div id="outline-container-orge615fec" class="outline-2">
<h2 id="orge615fec"><span class="section-number-2">9</span> Problem with AirLoc System</h2>
<div class="outline-text-2" id="text-9">
<p>
4 Airloc Levelers are used for the granite (figure <a href="#orgd24cfea">33</a>).
</p>
<div id="org6ddfc9a" class="figure">
<div id="orgd24cfea" class="figure">
<p><img src="img/airloc/IMG_20190618_155522.jpg" alt="IMG_20190618_155522.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 27: </span>AirLoc used for the granite (2120-KSKC)</p>
<p><span class="figure-number">Figure 33: </span>AirLoc used for the granite (2120-KSKC)</p>
</div>
<p>
They are probably not well leveled so that could explain the first modes at 11Hz and 17Hz.
They are probably <b>not well leveled</b> so that could explain the first modes at 11Hz and 17Hz.
</p>
</div>
</div>
<div id="outline-container-orgf013fb5" class="outline-2">
<h2 id="orgf013fb5"><span class="section-number-2">9</span> Spatial Mode Extraction</h2>
<div id="outline-container-orge98bc94" class="outline-2">
<h2 id="orge98bc94"><span class="section-number-2">10</span> Spatial Mode Extraction</h2>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-06-19 mer. 10:38</p>
<p class="date">Created: 2019-06-19 mer. 11:14</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>

231
modal-analysis/index.org
View File

@ -232,9 +232,132 @@ An exponential window (figure [[fig:window_response]]) is used for the response
#+attr_html: :width 500px
[[file:img/parameters/window_response.jpg]]
* FRF and COH Results
* 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)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
** Load Data
#+begin_src matlab
meas1_raw = load('modal_analysis/raw_data/Measurement1.mat');
#+end_src
** Raw Force Data
#+begin_src matlab :exports none
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]');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/raw_data_force.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:raw_data_force
#+CAPTION: Raw Force Data from Hammer Blow
[[file:figs/raw_data_force.png]]
#+begin_src matlab :exports none
xlim([22.1, 22.3]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/raw_data_force_zoom.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:raw_data_force_zoom
#+CAPTION: Raw Force Data from Hammer Blow - Zoom
[[file:figs/raw_data_force_zoom.png]]
** Raw Response Data
#+begin_src matlab :exports none
figure;
plot(time, meas1_raw.Track2);
xlabel('Time [s]');
ylabel('Acceleration [m/s2]');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/raw_data_acceleration.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:raw_data_acceleration
#+CAPTION: Raw Acceleration Data from Accelerometer
[[file:figs/raw_data_acceleration.png]]
#+begin_src matlab :exports none
xlim([22.1, 22.5]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/raw_data_acceleration_zoom.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:raw_data_acceleration_zoom
#+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');
#+end_src
** FRF and Coherence Results
#+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, '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');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/frf_result_example.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:frf_result_example
#+CAPTION: Example of one measured FRF
[[file:figs/frf_result_example.png]]
#+begin_src matlab :exports none
figure;
plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_Coh_2_1_RMS_Y_Val);
xlabel('Frequency [Hz]');
ylabel('Coherence');
#+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")
<<plt-matlab>>
#+end_src
#+NAME: fig:coh_result_example
#+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.
#+name: fig:mode1
#+caption: Mode 1
@ -276,6 +399,110 @@ An exponential window (figure [[fig:window_response]]) is used for the response
#+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
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
* Problem with AirLoc System
4 Airloc Levelers are used for the granite (figure [[fig:airloc]]).
@ -284,6 +511,6 @@ An exponential window (figure [[fig:window_response]]) is used for the response
#+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.
They are probably *not well leveled* so that could explain the first modes at 11Hz and 17Hz.
* Spatial Mode Extraction