From 3285e50315af87d01c11193d511022b5e5cf961a Mon Sep 17 00:00:00 2001
From: Thomas Dehaeze <dehaeze.thomas@gmail.com>
Date: Tue, 4 Feb 2025 15:38:20 +0100
Subject: [PATCH] Add prefix in footnotes

---
 modal-analysis.org | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/modal-analysis.org b/modal-analysis.org
index df2fe35..4319bb0 100644
--- a/modal-analysis.org
+++ b/modal-analysis.org
@@ -226,7 +226,7 @@ The obtained force and acceleration signals are described in Section ref:ssec:mo
 
 Three type of equipment are essential for a good modal analysis.
 First, /accelerometers/ are used to measure the response of the structure.
-Here, 3-axis accelerometers[fn:1] shown in figure ref:fig:modal_accelero_M393B05 are used.
+Here, 3-axis accelerometers[fn:modal_1] shown in figure ref:fig:modal_accelero_M393B05 are used.
 These accelerometers were glued to the micro-station using a thin layer of wax for best results [[cite:&ewins00_modal chapt. 3.5.7]].
 
 #+name: fig:modal_analysis_instrumentation
@@ -253,11 +253,11 @@ These accelerometers were glued to the micro-station using a thin layer of wax f
 #+end_subfigure
 #+end_figure
 
-Then, an /instrumented hammer/[fn:2] (figure ref:fig:modal_instrumented_hammer) is used to apply forces to the structure in a controlled manner.
+Then, an /instrumented hammer/[fn:modal_2] (figure ref:fig:modal_instrumented_hammer) is used to apply forces to the structure in a controlled manner.
 Tests were conducted to determine the most suitable hammer tip (ranging from a metallic one to a soft plastic one).
 The softer tip was found to give best results as it injects more energy in the low-frequency range where the coherence was low, such that the overall coherence was improved.
 
-Finally, an /acquisition system/[fn:3] (figure ref:fig:modal_oros) is used to acquire the injected force and response accelerations in a synchronized manner and with sufficiently low noise.
+Finally, an /acquisition system/[fn:modal_3] (figure ref:fig:modal_oros) is used to acquire the injected force and response accelerations in a synchronized manner and with sufficiently low noise.
 
 ** Structure Preparation and Test Planing
 <<ssec:modal_test_preparation>>
@@ -678,7 +678,7 @@ Writing this in matrix form for the four points gives eqref:eq:modal_cart_to_acc
 \end{array}\right]
 \end{equation}
 
-Provided that the four sensors are properly located, the system of equation eqref:eq:modal_cart_to_acc can be solved by matrix inversion[fn:5].
+Provided that the four sensors are properly located, the system of equation eqref:eq:modal_cart_to_acc can be solved by matrix inversion[fn:modal_5].
 The motion of the solid body expressed in a chosen frame $\{O\}$ can be determined using equation eqref:eq:modal_determine_global_disp.
 Note that this matrix inversion is equivalent to resolving a mean square problem.
 Therefore, having more accelerometers permits better approximation of the motion of a solid body.
@@ -1079,7 +1079,7 @@ The levelers were then better adjusted.
 #+attr_latex: :width 0.6\linewidth
 [[file:figs/modal_airlock_picture.jpg]]
 
-The modal parameter extraction is made using a proprietary software[fn:4].
+The modal parameter extraction is made using a proprietary software[fn:modal_4].
 For each mode $r$ (from $1$ to the number of considered modes $m=16$), it outputs the frequency $\omega_r$, the damping ratio $\xi_r$, the eigenvectors $\{\phi_{r}\}$ (vector of complex numbers with a size equal to the number of measured acrshort:dof $n=69$, see equation eqref:eq:modal_eigenvector) and a scaling factor $a_r$.
 
 \begin{equation}\label{eq:modal_eigenvector}
@@ -1330,8 +1330,8 @@ colors = colororder;
 
 * Footnotes
 
-[fn:5]As this matrix is in general non-square, the Moore–Penrose inverse can be used instead.
-[fn:4]NVGate software from OROS company.
-[fn:3]OROS OR36. 24bits signal-delta ADC.
-[fn:2]Kistler 9722A2000. Sensitivity of $2.3\,mV/N$ and measurement range of $2\,kN$
-[fn:1]PCB 356B18. Sensitivity is $1\,V/g$, measurement range is $\pm 5\,g$ and bandwidth is $0.5$ to $5\,\text{kHz}$.
+[fn:modal_5]As this matrix is in general non-square, the Moore–Penrose inverse can be used instead.
+[fn:modal_4]NVGate software from OROS company.
+[fn:modal_3]OROS OR36. 24bits signal-delta ADC.
+[fn:modal_2]Kistler 9722A2000. Sensitivity of $2.3\,mV/N$ and measurement range of $2\,kN$
+[fn:modal_1]PCB 356B18. Sensitivity is $1\,V/g$, measurement range is $\pm 5\,g$ and bandwidth is $0.5$ to $5\,\text{kHz}$.