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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <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 http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Modal Analysis</title> <title>Modal Analysis</title>
@ -280,50 +280,55 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgac37ea1">1. Goal</a></li> <li><a href="#org1d79a68">1. Goal</a></li>
<li><a href="#org2c806fc">2. Type of Model</a></li> <li><a href="#orgde6e655">2. Type of Model</a></li>
<li><a href="#orgc645667">3. Instrumentation Used</a></li> <li><a href="#org9414b8d">3. Instrumentation Used</a></li>
<li><a href="#org1a9bf2b">4. Structure Preparation and Test Planning</a> <li><a href="#org521ef27">4. Structure Preparation and Test Planning</a>
<ul> <ul>
<li><a href="#orgec92624">4.1. Structure Preparation</a></li> <li><a href="#orga7b6b16">4.1. Structure Preparation</a></li>
<li><a href="#orgf3e7d52">4.2. Test Planing</a></li> <li><a href="#org62eba0c">4.2. Test Planing</a></li>
<li><a href="#orge605474">4.3. Location of the Accelerometers</a></li> <li><a href="#org9c54744">4.3. Location of the Accelerometers</a></li>
<li><a href="#org9371de2">4.4. Hammer Impacts</a></li> <li><a href="#org2ba755b">4.4. Hammer Impacts</a></li>
</ul> </ul>
</li> </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> <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> </ul>
</li> </li>
<li><a href="#orga28022b">6. FRF and COH Results</a></li> <li><a href="#org01620a5">7. Mode Shapes</a></li>
<li><a href="#orgd5a7271">7. Mode Shapes</a></li> <li><a href="#org7403c04">8. Obtained Modal Matrices</a></li>
<li><a href="#org56702cf">8. Problem with AirLoc System</a></li> <li><a href="#orge615fec">9. Problem with AirLoc System</a></li>
<li><a href="#orgf013fb5">9. Spatial Mode Extraction</a></li> <li><a href="#orge98bc94">10. Spatial Mode Extraction</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgac37ea1" class="outline-2"> <div id="outline-container-org1d79a68" class="outline-2">
<h2 id="orgac37ea1"><span class="section-number-2">1</span> Goal</h2> <h2 id="org1d79a68"><span class="section-number-2">1</span> Goal</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <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> </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><img src="img/nass_picture.png" alt="nass_picture.png" width="500px" />
</p> </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> <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> </div>
<p> <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> </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><img src="img/vibration_analysis_procedure.png" alt="vibration_analysis_procedure.png" width="400px" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Vibration Analysis Procedure</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> </div>
<div id="outline-container-org2c806fc" class="outline-2"> <div id="outline-container-orgde6e655" class="outline-2">
<h2 id="org2c806fc"><span class="section-number-2">2</span> Type of Model</h2> <h2 id="orgde6e655"><span class="section-number-2">2</span> Type of Model</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
The model that we want to obtain is a <b>multi-body model</b>. 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>. 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>
<p> <p>
@ -367,7 +372,7 @@ In the simscape model, the solid bodies are:
</ul> </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><img src="img/nass_solidworks.png" alt="nass_solidworks.png" width="800px" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>CAD view of the ID31 Micro-Station</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> </div>
<div id="outline-container-orgc645667" class="outline-2"> <div id="outline-container-org9414b8d" class="outline-2">
<h2 id="orgc645667"><span class="section-number-2">3</span> Instrumentation Used</h2> <h2 id="org9414b8d"><span class="section-number-2">3</span> Instrumentation Used</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
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:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>An <b>acquisition system</b> (OROS) with 24bits ADCs (figure <a href="#orga72e510">4</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="#orge04521f">5</a>) with parameters shown on table <a href="#org69d60d7">1</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="#org809d290">6</a>) (figure <a href="#org0fe6440">7</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> </ul>
<div id="orga72e510" class="figure"> <div id="org754b9bb" class="figure">
<p><img src="img/instrumentation/oros.png" alt="oros.png" width="500px" /> <p><img src="img/instrumentation/oros.png" alt="oros.png" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Acquisition system: OROS</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> </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><img src="img/instrumentation/accelero_M393B05.png" alt="accelero_M393B05.png" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Accelerometer used: M393B05</p> <p><span class="figure-number">Figure 5: </span>Accelerometer used: M393B05</p>
</div> </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> <caption class="t-above"><span class="table-number">Table 1:</span> 393B05 Accelerometer Data Sheet</caption>
<colgroup> <colgroup>
@ -459,14 +464,14 @@ It excites more the low frequency range where the coherence is low, the overall
</p> </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><img src="img/instrumentation/instrumented_hammer.png" alt="instrumented_hammer.png" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Instrumented Hammer</p> <p><span class="figure-number">Figure 6: </span>Instrumented Hammer</p>
</div> </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><img src="img/instrumentation/hammer_tips.png" alt="hammer_tips.png" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Hammer tips</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> </div>
<div id="outline-container-org1a9bf2b" class="outline-2"> <div id="outline-container-org521ef27" class="outline-2">
<h2 id="org1a9bf2b"><span class="section-number-2">4</span> Structure Preparation and Test Planning</h2> <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 class="outline-text-2" id="text-4">
</div> </div>
<div id="outline-container-orgec92624" class="outline-3"> <div id="outline-container-orga7b6b16" class="outline-3">
<h3 id="orgec92624"><span class="section-number-3">4.1</span> Structure Preparation</h3> <h3 id="orga7b6b16"><span class="section-number-3">4.1</span> Structure Preparation</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<p> <p>
All the stages are turned ON. 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> </div>
<div id="outline-container-orgf3e7d52" class="outline-3"> <div id="outline-container-org62eba0c" class="outline-3">
<h3 id="orgf3e7d52"><span class="section-number-3">4.2</span> Test Planing</h3> <h3 id="org62eba0c"><span class="section-number-3">4.2</span> Test Planing</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
<p> <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). 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> </div>
<div id="outline-container-orge605474" class="outline-3"> <div id="outline-container-org9c54744" class="outline-3">
<h3 id="orge605474"><span class="section-number-3">4.3</span> Location of the Accelerometers</h3> <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"> <div class="outline-text-3" id="text-4-3">
<p> <p>
4 tri-axis accelerometers are used for each solid body. 4 tri-axis accelerometers are used for each solid body.
@ -580,29 +585,29 @@ The position of the accelerometers are:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>4 on the first granite</li> <li>4 on the first granite</li>
<li>4 on the second granite (figure <a href="#orgf735e72">8</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="#org9df7efa">9</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 tilt stage</li>
<li>4 on top of the spindle</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> </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><img src="img/accelerometers/accelerometers_granite2_overview.jpg" alt="accelerometers_granite2_overview.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Accelerometers located on the top granite</p> <p><span class="figure-number">Figure 8: </span>Accelerometers located on the top granite</p>
</div> </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><img src="img/accelerometers/accelerometers_ty_overview.jpg" alt="accelerometers_ty_overview.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Accelerometers located on top of the translation stage</p> <p><span class="figure-number">Figure 9: </span>Accelerometers located on top of the translation stage</p>
</div> </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><img src="img/accelerometers/accelerometers_hexa_overview.jpg" alt="accelerometers_hexa_overview.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Accelerometers located on the Hexapod</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> </div>
<div id="outline-container-org9371de2" class="outline-3"> <div id="outline-container-org2ba755b" class="outline-3">
<h3 id="org9371de2"><span class="section-number-3">4.4</span> Hammer Impacts</h3> <h3 id="org2ba755b"><span class="section-number-3">4.4</span> Hammer Impacts</h3>
<div class="outline-text-3" id="text-4-4"> <div class="outline-text-3" id="text-4-4">
<p> <p>
Only 3 impact points are used. Only 3 impact points are used.
</p> </p>
<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> </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><img src="img/impacts/hammer_x.gif" alt="hammer_x.gif" width="300px" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Hammer Blow in the X direction</p> <p><span class="figure-number">Figure 11: </span>Hammer Blow in the X direction</p>
</div> </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><img src="img/impacts/hammer_y.gif" alt="hammer_y.gif" width="300px" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Hammer Blow in the Y direction</p> <p><span class="figure-number">Figure 12: </span>Hammer Blow in the Y direction</p>
</div> </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><img src="img/impacts/hammer_z.gif" alt="hammer_z.gif" width="300px" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Hammer Blow in the Z direction</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> </div>
<div id="outline-container-orgc76dac6" class="outline-2"> <div id="outline-container-org9bef537" class="outline-2">
<h2 id="orgc76dac6"><span class="section-number-2">5</span> Measurements</h2> <h2 id="org9bef537"><span class="section-number-2">5</span> Signal Processing</h2>
<div class="outline-text-2" id="text-5"> <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> <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> </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><img src="img/parameters/general_parameters.jpg" alt="general_parameters.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>General Acquisition Settings</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>
<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>
<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> </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><img src="img/parameters/window_force.jpg" alt="window_force.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Window used for the force signal</p> <p><span class="figure-number">Figure 15: </span>Window used for the force signal</p>
</div> </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><img src="img/parameters/window_response.jpg" alt="window_response.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 16: </span>Window used for the response signal</p> <p><span class="figure-number">Figure 16: </span>Window used for the response signal</p>
</div> </div>
</div> </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>
<div id="outline-container-orga28022b" class="outline-2"> <div id="outline-container-orgf4cdb9c" class="outline-3">
<h2 id="orga28022b"><span class="section-number-2">6</span> FRF and COH Results</h2> <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>
<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"> <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><img src="img/modes/mode1.gif" alt="mode1.gif" />
</p> </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>
<div id="org8d04700" class="figure"> <div id="org67a662e" class="figure">
<p><img src="img/modes/mode2.gif" alt="mode2.gif" /> <p><img src="img/modes/mode2.gif" alt="mode2.gif" />
</p> </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>
<div id="orgf6bbcc2" class="figure"> <div id="org442b3c1" class="figure">
<p><img src="img/modes/mode3.gif" alt="mode3.gif" /> <p><img src="img/modes/mode3.gif" alt="mode3.gif" />
</p> </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>
<div id="org65681ff" class="figure"> <div id="org874bdc2" class="figure">
<p><img src="img/modes/mode4.gif" alt="mode4.gif" /> <p><img src="img/modes/mode4.gif" alt="mode4.gif" />
</p> </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>
<div id="orgf9a0639" class="figure"> <div id="org17b0003" class="figure">
<p><img src="img/modes/mode5.gif" alt="mode5.gif" /> <p><img src="img/modes/mode5.gif" alt="mode5.gif" />
</p> </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>
<div id="org368c756" class="figure"> <div id="orge792930" class="figure">
<p><img src="img/modes/mode6.gif" alt="mode6.gif" /> <p><img src="img/modes/mode6.gif" alt="mode6.gif" />
</p> </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>
<div id="org0664fec" class="figure"> <div id="org51bf469" class="figure">
<p><img src="img/modes/mode7.gif" alt="mode7.gif" /> <p><img src="img/modes/mode7.gif" alt="mode7.gif" />
</p> </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>
<div id="org65c79b2" class="figure"> <div id="orgbbbf537" class="figure">
<p><img src="img/modes/mode8.gif" alt="mode8.gif" /> <p><img src="img/modes/mode8.gif" alt="mode8.gif" />
</p> </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>
<div id="org261f452" class="figure"> <div id="orgda7c6b4" class="figure">
<p><img src="img/modes/mode9.gif" alt="mode9.gif" /> <p><img src="img/modes/mode9.gif" alt="mode9.gif" />
</p> </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>
<div id="org4881e36" class="figure"> <div id="org3deb93b" class="figure">
<p><img src="img/modes/mode10.gif" alt="mode10.gif" /> <p><img src="img/modes/mode10.gif" alt="mode10.gif" />
</p> </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>
</div> </div>
<div id="outline-container-org56702cf" class="outline-2"> <div id="outline-container-org7403c04" class="outline-2">
<h2 id="org56702cf"><span class="section-number-2">8</span> Problem with AirLoc System</h2> <h2 id="org7403c04"><span class="section-number-2">8</span> Obtained Modal Matrices</h2>
<div class="outline-text-2" id="text-8"> <div class="outline-text-2" id="text-8">
<p> <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> </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><img src="img/airloc/IMG_20190618_155522.jpg" alt="IMG_20190618_155522.jpg" width="500px" />
</p> </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> </div>
<p> <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> </p>
</div> </div>
</div> </div>
<div id="outline-container-orgf013fb5" class="outline-2"> <div id="outline-container-orge98bc94" class="outline-2">
<h2 id="orgf013fb5"><span class="section-number-2">9</span> Spatial Mode Extraction</h2> <h2 id="orge98bc94"><span class="section-number-2">10</span> Spatial Mode Extraction</h2>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <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> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </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 #+attr_html: :width 500px
[[file:img/parameters/window_response.jpg]] [[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 * 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 #+name: fig:mode1
#+caption: Mode 1 #+caption: Mode 1
@ -276,6 +399,110 @@ An exponential window (figure [[fig:window_response]]) is used for the response
#+caption: Mode 10 #+caption: Mode 10
[[file:img/modes/mode10.gif]] [[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 * Problem with AirLoc System
4 Airloc Levelers are used for the granite (figure [[fig:airloc]]). 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 #+attr_html: :width 500px
[[file:img/airloc/IMG_20190618_155522.jpg]] [[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 * Spatial Mode Extraction