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<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Maximizing the Torsional Modal Eigenfrequency</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3"><table class = "DocHeaderIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract">
<span class = "shortdesc">Often it is needed to increase a specific eigenfrequency in
the eigenfrequency spectrum belonging to a certain eigenmode. In this
case, a specific eigenfrequency is defined using <code class = "ph codeph">TYPE = DYN_FREQ</code>.
</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-sizing-TasksModAna-maxTorsFreq__tso-c-usr-sizing-TasksModAna-minTorsFreq-optProb" id = "toc_rg" title = "">Formulation of the Optimization Problem</a></li><li><a href = "#tso-c-usr-sizing-TasksModAna-maxTorsFreq__tso-c-usr-sizing-TasksModAna-minTorsFreq-Res" id = "toc_rg" title = "">Results</a></li></ul>
</p></td></tr></table></td><td class = "DocHeader2"><table class = "DocTopicsSeeAlso" id = "table13"><tr><td class = "TopicsTitle">See Also</td></tr><tr><td><a title = "This section describes the theory of eigenfrequency." href = "tso-c-usr-terms-eigfreqOvw.htm#tso-c-usr-terms-eigfreqOvw">Overview of Eigenfrequency</a></td></tr></table></td></tr></table>




<div class = "body conbody">
  
<div class = "section" id = "tso-c-usr-sizing-TasksModAna-maxTorsFreq__tso-c-usr-sizing-TasksModAna-minTorsFreq-optProb"><h2 class = "title sectiontitle">Formulation of the Optimization Problem</h2>

<p>The optimization task is to maximize the second torsional modal eigenfrequency
with a volume constraint of 100% and without any boundaries.  </p>
<table class = "table" id = "tso-c-usr-sizing-TasksModAna-maxTorsFreq__aa782214"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
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<td class = "entry"><p>Model:</p><br/><img class = "image" src = "../TsoUserImages/size_typtasks_MinVol_modaltors_Obj2.png" width = "300"/><br/></td>
</tr>
<tr class = "row">
<td class = "entry"><p>f=21.6Hz:</p><br/><img class = "image" src = "../TsoUserImages/size_typtasks_MinVol_modaltors_Obj1.png" width = "300"/><br/></td>
</tr>
<tr class = "row">
<td class = "entry"><p>f=25.8Hz(must be maximized):   </p><br/><img class = "image" src = "../TsoUserImages/size_typtasks_MinVol_modaltors_Obj2a.png" width = "300"/><br/></td>
</tr>
<tr class = "row">
<td class = "entry"><p>f=29.6Hz:</p><br/><img class = "image" src = "../TsoUserImages/size_typtasks_MinVol_modaltors_Obj4.png" width = "300"/><br/></td>
</tr>
<tr class = "row">
<td class = "entry"><p>f=34.2Hz:</p><br/><img class = "image" src = "../TsoUserImages/size_typtasks_MinVol_modaltors_Obj3.png" width = "300"/><br/></td>
</tr>
<tr class = "row">
<td class = "entry"><p>f=36.3Hz:</p><br/><img class = "image" src = "../TsoUserImages/size_typtasks_MinVol_modaltors_Obj5.png" width = "300"/><br/></td>
</tr>
<tr class = "row">
<td class = "entry"><p>f=37.5Hz:</p><br/><img class = "image" src = "../TsoUserImages/size_typtasks_MinVol_modaltors_Obj6.png" width = "300"/><br/></td>
</tr>
</tbody></table>

<p>In the above figure, you can see the model and the first six modal
eigenfrequencies.</p>
</div>

<div class = "section" id = "tso-c-usr-sizing-TasksModAna-maxTorsFreq__tso-c-usr-sizing-TasksModAna-minTorsFreq-Res"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Results</h2>

<p>As shown in the next figure, the original mode 2 is now mode 4 maximizing the torsional
    eigenfrequency.</p>
<table class = "table" id = "tso-c-usr-sizing-TasksModAna-maxTorsFreq__aa782177"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" src = "../TsoUserImages/aa0bef64.jpg" width = "450"/><br/></td>
</tr>
</tbody></table>

<p> When optimizing a specific eigenfrequency, the order of the eigenfrequencies
might change during the optimization iterations.</p>
<p>Consequently, the eigenfrequencies might must be tracked during
the optimization iterations. </p>
<p>The tracking is done using mode tracking as described in
<a class = "xref" href = "tso-c-usr-sizing-Settings-ModeTrack.htm#tso-c-usr-sizing-Settings-ModeTrack" title = "It is possible to apply a simple mode tracking function for the modal analysis using the modal assurance criterion (MAC) including a mass weighting.">Mode Tracking</a>.</p>
<p>By default, the modes are not tracked during the optimization. Mode
tracking is activated in <code class = "ph codeph">OPT_PARAM</code> command:</p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
 ID_NAME  = 2nd_lowest_eigenfrequency
 DEF_TYPE = SYSTEM
 TYPE     = DYN_FREQ
 LC_SET   = MODAL, ALL, 2
END_

OBJ_FUNC
 ID_NAME = maximize_single_eigenfrequency
 DRESP   = 2nd_lowest_eigenfrequency
 TARGET  = MAX
END_

OPT_PARAM
 ID_NAME      = opt_params
 OPTIMIZE     = maximize_single_eigenfrequency
 MODETRACKING = ON
 MODENUMBERS  = 8
END_
</code>
</pre>
<p>For this example, at least 8 eigenfrequencies should be requested in the
finite element input model defined by the user.</p>


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