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Update modal extraction

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Thomas Dehaeze
2019-07-16 11:09:14 +02:00
parent c0641f7865
commit e4d8712c94
8 changed files with 686 additions and 481 deletions
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modal-analysis/index.html
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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>
<!-- 2019-07-05 ven. 10:17 -->
<!-- 2019-07-12 ven. 11:24 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Modal Analysis of the ID31 Micro-Station</title>
@@ -246,6 +246,28 @@ for the JavaScript code in this tag.
}
/*]]>*///-->
</script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
displayAlign: "center",
displayIndent: "0em",
"HTML-CSS": { scale: 100,
linebreaks: { automatic: "false" },
webFont: "TeX"
},
SVG: {scale: 100,
linebreaks: { automatic: "false" },
font: "TeX"},
NativeMML: {scale: 100},
TeX: { equationNumbers: {autoNumber: "AMS"},
MultLineWidth: "85%",
TagSide: "right",
TagIndent: ".8em"
}
});
</script>
<script type="text/javascript"
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML"></script>
</head>
<body>
<div id="org-div-home-and-up">
@@ -256,22 +278,22 @@ for the JavaScript code in this tag.
<h1 class="title">Modal Analysis of the ID31 Micro-Station</h1>
<p>
The goal is to experimentally extract a <b>Spatial Model</b> (mass, damping, stiffness) of the structure (shown on figure <a href="#org811aaee">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="#org4a31989">1</a>) in order to tune the Multi-Body model.
</p>
<div id="org811aaee" class="figure">
<div id="org4a31989" 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="#org60c2278">2</a> where we go from left to right.
The procedure is represented on figure <a href="#org4a4053c">2</a> where we go from left to right.
</p>
<div id="org60c2278" class="figure">
<div id="org4a4053c" 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>
@@ -294,6 +316,107 @@ 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.
</p>
<table id="org890b40f" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Terminology for further analysis</caption>
<colgroup>
<col class="org-center" />
<col class="org-left" />
<col class="org-center" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-center">Symbol</th>
<th scope="col" class="org-left">Meaning</th>
<th scope="col" class="org-center">Value</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-center">\(S\)</td>
<td class="org-left">Number of solid body considered</td>
<td class="org-center">6</td>
</tr>
<tr>
<td class="org-center">\(M\)</td>
<td class="org-left">Number of accelerometers</td>
<td class="org-center">23</td>
</tr>
<tr>
<td class="org-center">\(N\)</td>
<td class="org-left">Number of identified modes</td>
<td class="org-center">21</td>
</tr>
<tr>
<td class="org-center">\(p\)</td>
<td class="org-left">Number of frequency points</td>
<td class="org-center">801</td>
</tr>
<tr>
<td class="org-center">\(E\)</td>
<td class="org-left">Number of excitation</td>
<td class="org-center">3</td>
</tr>
</tbody>
</table>
<table id="orgbda6b99" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Terminology for further analysis</caption>
<colgroup>
<col class="org-center" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-center">Symbol</th>
<th scope="col" class="org-left">Meaning</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-center">\(\Lambda\)</td>
<td class="org-left">Complex eigen value matrix</td>
</tr>
<tr>
<td class="org-center">\([\Psi]\)</td>
<td class="org-left">Complex eigen vector matrix</td>
</tr>
<tr>
<td class="org-center">\(\omega_r\)</td>
<td class="org-left">Eigen frequency of mode \(r\) [rad/s]</td>
</tr>
<tr>
<td class="org-center">\(\xi_r\)</td>
<td class="org-left">Modal damping for mode \(r\)</td>
</tr>
<tr>
<td class="org-center">\(\{\psi\}_r\)</td>
<td class="org-left">Complex mode shape of mode \(r\)</td>
</tr>
<tr>
<td class="org-center">\([M], [C], [K]\)</td>
<td class="org-left">Mass, damping and stiffness matrices</td>
</tr>
<tr>
<td class="org-center">\(a_r\)</td>
<td class="org-left">"Modal A" for mode \(r\)</td>
</tr>
</tbody>
</table>
<p>
The modal analysis of the ID31 Micro-station thus consists of several parts:
@@ -307,7 +430,7 @@ The modal analysis of the ID31 Micro-station thus consists of several parts:
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-07-05 ven. 10:17</p>
<p class="date">Created: 2019-07-12 ven. 11:24</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>