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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>Frequency Spectrum</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3" colspan = "2"><table class = "DocThemeIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract">
<span class = "shortdesc">Frequency responses can be obtained in several ways in
<span class = "ph">ANSYS®</span>.
They are discussed within this section.</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-limitations" id = "toc_rg" title = "">Limitations</a></li><li><a href = "#tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-ovw" id = "toc_rg" title = "">Overview</a></li><li><a href = "#tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-directsol" id = "toc_rg" title = "">Direct Solution</a></li><li><a href = "#tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-moddec" id = "toc_rg" title = "">Modal Decomposition</a></li><li><a href = "#tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-dampmat" id = "toc_rg" title = "">General Damping Matrices in <span class = "ph">ANSYS®</span></a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">

<div class = "section" id = "tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-limitations"><h2 class = "title sectiontitle">Limitations</h2>

<p>Currently frequency responses are allowed only for sizing optimization.</p>
</div>


<div class = "section" id = "tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-ovw"><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">Overview</h2>

<p>
Frequency response is obtained using <code class = "ph codeph">ANTYPE, 3</code> or
<code class = "ph codeph">ANTYPE,SPECTR</code> in the CDB finite element input file. The different
solution methods for calculating the spectrum in <span class = "ph">ANSYS®</span>
are activated using <code class = "ph codeph">HROPT</code>. The three following methods are supported in
<span class = "ph">Tosca Structure</span>:
</p>
<ul class = "ul">
<li class = "li"><code class = "ph codeph">HROPT,FULL</code> <p>This is the full solution method.</p></li>
<li class = "li"><code class = "ph codeph"> HROPT,REDUC</code>
<ul class = "ul">
<li class = "li">Reduced solution method (deals only with main nodes, can be viewed as an extension of the Mode Superposition Method)</li>
<li class = "li">
By default, the reduced solution method writes the reduced results to the
<code class = "ph codeph"> RFRQ</code> file. However, the reduced results must
be expanded to the entire results in the RST file. Therefore, the following has
to be added in the CDB finite element input file:
<ul class = "ul">
<li class = "li"><code class = "ph codeph">EXPASS,ON</code> for obtaining the response for all nodes.</li>
<li class = "li"><code class = "ph codeph">NUMEXP</code> for defining the frequency range to be expanded.</li>
<li class = "li">
<code class = "ph codeph">HROUT, ON, OFF</code>, for
printing the real and imaginary components (<code class = "ph codeph">ON</code> is also default)
and for uniform spacing of the excitation frequencies (<code class = "ph codeph">OFF</code> is
also default). <code class = "ph codeph">HROUT, ON, ON</code> for eigenvalue-dependent spacing is also allowed.
</li>
</ul>
</li>
</ul>
</li>
<li class = "li">
<code class = "ph codeph">HROPT,MSUP</code>
<p>
Superposition, the most used option for large models because it is
very fast. However, it is requiring that the eigenfrequencies (ANTYPE, 2 and
the number of eigenfrequencies) are initially calculated.
</p>
<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent">
<p>
This method can give quite wrong results for low-excitation frequencies corresponding to
the almost static <span class = "ph">load case</span>:
</p>
<ul class = "ul">
<li class = "li"><code class = "ph codeph">EXPASS,ON</code> for obtaining the response for all nodes.</li>
<li class = "li"><code class = "ph codeph">NUMEXP</code> for defining the frequency range to be expanded.</li>
<li class = "li">
<code class = "ph codeph">HROUT, ON, OFF</code>, for printing
the real and imaginary components (<code class = "ph codeph">ON</code> is also default) and for
uniform spacing of the excitation frequencies (<code class = "ph codeph">OFF</code> is also
default). <code class = "ph codeph">HROUT, ON, ON</code> for eigenvalue-dependent spacing is also
allowed.
</li>
</ul>
</span></td></tr></table>

</li>
</ul>
</div>


<div class = "section" id = "tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-directsol"><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">Direct Solution</h2>

<p>
In the following, an example of a part of a <span class = "ph">load case</span>
file (file.s*) using the solution method <code class = "ph codeph">HROPT,FULL</code> is shown:
</p>
<pre class = "codeblock">
<code class = "ph codeph">
.........
ANTYPE, 3 ! frequency response
ALPHAD, 0.01 ! Viscous mass damping
BETAD, 0.02 ! Viscous stiffness damping
DMPRAT, 0.03 ! Structural stiffness damping
HROPT,FULL ! Direct solution method
HROUT,ON,OFF ! Uniform spacing (default)
NSUBST, 405 ! Number of substeps
HARFRQ,0,500 ! Frequency range
OUTPR,ALL,NONE ! No output in ASCII format
.........
</code>
</pre>
<p>Below an example of a part of a CDB file using <span class = "ph">load cases</span> based on
<pre class = "codeblock">HROPT,FULL</pre> is shown:</p>
<pre class = "codeblock">
<code class = "ph codeph">
................
/GO
FINISH
! ---------------------------------------------------
/SOLU
HROUT,ON,OFF ! Both real and imaginary part
OUTPR,ALL,NONE ! No output in ASCII format
LSSOLVE,1,1,12 ! In this case 12 load cases
FINISH
................
</code>
</pre>
</div>


<div class = "section" id = "tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-moddec"><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">Modal Decomposition</h2>

<p>
In the following, an example of a part of a <span class = "ph">load case</span>
file (file.s*) using the solution method <code class = "ph codeph">HROPT,MSUP</code> (or <code class = "ph codeph">HROPT,REDUC</code>) is shown:
</p>
<pre class = "codeblock">
<code class = "ph codeph">.........
ANTYPE, 3 ! frequency response
ALPHAD, 0.01 ! Viscous mass damping
BETAD, 0.02 ! Viscous stiffness damping
DMPRAT, 0.03 ! Structural stiffness damping
HROPT,MSUP,25,1 ! Mode superposition method
HROUT,ON,OFF ! Uniform spacing (default)
NSUBST, 405 ! Number of substeps
HARFRQ,0,500 ! Frequency range
OUTPR,ALL,NONE ! No output in ASCII format
.........
</code>
</pre>
<p>
An example of a part of a CDB file using <span class = "ph">load cases</span> based on
<code class = "ph codeph">HROPT,REDUC</code> or <code class = "ph codeph">HROPT,MSUP</code> is shown below.
</p>
<div class = "note"><span class = "run-in.note">Note:
			</span><span class = "notecontent"><p>
The CDB file should have the name model.cdb in this example. If another file name for the
CDB file is applied, then the file name "model" should be substituted with the other file name.
</p></span></div>

<p>
In the given example, the frequency range is going from 0 Hz to 500 Hz
using 105 increments. The user can also apply <code class = "ph codeph">NUMEXP,ALL</code>.
<pre class = "codeblock">
<code class = "ph codeph">
..........
/GO
FINISH
! ---------------------------------------------------
! Modal (Eigenfrequency) solution
/SOLU
LSSOLVE,1,1,1
/COPY,file,rst,,model_1,rst
FINISH
! ---------------------------------------------------
! Frequency response solution
! ---------------------------------------------------
! Load case 2: Frequency response 1
! use the results of the modal analysis
/SOLU
/COPY,model_1,rst,,file,rst
LSSOLVE,2,2,1
FINISH
! expansion of the solution
/SOLU
/assign,rst,model_2,rst
EXPASS,ON
OUTPR,ALL,NONE ! No output in ASCII format
NUMEXP, 105, 0.0, 500.0 ! the frequency range to expand
HROUT,ON,OFF ! both real and imaginary part
SOLVE
FINISH
! ---------------------------------------------------
! Load case 3: Frequency response loadcase 2
! use the results of the modal analysis
/SOLU
/COPY,model_1,rst,,file,rst
LSSOLVE,3,3,1
FINISH
! expansion of the solution
/SOLU
/assign,rst,model_3,rst
EXPASS,ON
OUTPR,ALL,NONE ! No output in ASCII format
NUMEXP, 105, 0.0, 500.0 ! the frequency range to expand
HROUT,ON,OFF ! both real and imaginary part
SOLVE
FINISH
! ---------------------------------------------------
! Load case 4: Frequency response loadcase 3
! use the results of the modal analysis
/SOLU
/COPY,model_1,rst,,file,rst
LSSOLVE,4,4,1
FINISH
! expansion of the solution
/SOLU
/assign,rst,model_4,rst
EXPASS,ON
OUTPR,ALL,NONE ! No output in ASCII format
NUMEXP, 105, 0.0, 500.0 ! the frequency range to expand
HROUT,ON,OFF ! both real and imaginary part
SOLVE
FINISH
..............
</code>
</pre>
</p>
<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent">
<p>
<ul class = "ul">
<li class = "li">Significant improvement
in the CPU-time is obtained using the following command in each <span class = "ph">load case</span>. This
ensures that no ASCII information is written as output. Therefore, adding this
command in each <span class = "ph">load case</span> is strongly recommended.:
<pre class = "codeblock">
<code class = "ph codeph">
OUTPR,ALL,NONE ! No output in ASCII format
</code>
</pre>
</li>
<li class = "li">
Significant improvement in the CPU-time is obtained using the following command in each <span class = "ph">load case</span>. This
ensures that only nodal results are written to the database. Therefore, adding these commands in each <span class = "ph">load case</span> is strongly recommended:
<pre class = "codeblock"><code class = "ph codeph">OUTRES,ALL,NONE ! No output in binary format (rst-file)
OUTRES,NSOL,ALL ! Output only node results (displacements)
</code></pre>
</li>
<li class = "li">
Prescribed displacements and thereby indirectly
velocities, and accelerations for <span class = "ph">ANSYS®</span>
are supported in frequency response using the command <code class = "ph codeph">D</code> for
defining degree of freedom constraints at nodes. Other types of prescribed
displacements, velocities, and accelerations for
<span class = "ph">ANSYS®</span> are not supported.
</li>
</ul>
</p>
</span></td></tr></table>

</div>


<div class = "section" id = "tso-c-usr-solver-ansys-freqspec__tso-c-usr-solver-ansys-dampmat"><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">General Damping Matrices in <span class = "ph">ANSYS®</span></h2>

<p>The general damping matrix [C] of the structure can be written as</p>

<table class = "table" id = "tso-c-usr-solver-ansys-freqspec__table_9142E8E4B60343EA81F4338C75C1B620"><caption/><colgroup><col style = "width:100%"/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">C</mi><mo class = "- topic/foreign ">]</mo></mrow><mo class = "- topic/foreign ">=</mo><mi class = "- topic/foreign ">α</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">M</mi><mo class = "- topic/foreign ">]</mo></mrow><mo class = "- topic/foreign ">+</mo><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi class = "- topic/foreign ">β</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">K</mi><mo class = "- topic/foreign ">]</mo><mo class = "- topic/foreign ">+</mo><munderover class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi><mo class = "- topic/foreign ">=</mo><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">N</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">m</mi></mrow></msub></mrow></munderover><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mstyle displaystyle = "true" class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">m</mi></mrow></msubsup></mrow></mstyle><mo class = "- topic/foreign ">+</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow></mfrac><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ξ</mi></mrow></msubsup><mo class = "- topic/foreign ">)</mo></mrow><mo class = "- topic/foreign ">[</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">K</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi></mrow></msub><mo class = "- topic/foreign ">]</mo><mo class = "- topic/foreign ">]</mo></mrow><mo class = "- topic/foreign ">+</mo><mstyle displaystyle = "true" class = "- topic/foreign "><mrow class = "- topic/foreign "><munderover class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi><mo class = "- topic/foreign ">=</mo><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">N</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub></mrow></munderover><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">C</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub><mo class = "- topic/foreign ">]</mo><mo class = "- topic/foreign ">+</mo><mo class = "- topic/foreign ">[</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">C</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ξ</mi></mrow></msub><mo class = "- topic/foreign ">]</mo></mrow></mrow></mstyle></mrow></math></span>           </td>
</tr>
</tbody></table>

<p>with</p>

<table class = "table" id = "tso-c-usr-solver-ansys-freqspec__table_1135919692C24BBDA809EF23C36BE996"><caption/><colgroup><col style = "width:29.49852507374631%"/><col style = "width:70.50147492625369%"/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">K</mi><mo class = "- topic/foreign ">]</mo></mrow></mrow></math></span>=</td>
<td class = "entry"><p>structural stiffness matrix</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">M</mi><mo class = "- topic/foreign ">]</mo></mrow></math></span>=</td>
<td class = "entry"><p>structural mass matrix</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow></math></span>=</td>
<td class = "entry"><p>circular excitation frequency</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow></math></span>=</td>
<td class = "entry"><p>mass matrix multiplier for viscous damping</p>
                      <p>(input in <span class = "ph">ANSYS®</span> using the ALPHAD command)</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow></math></span>=</td>
<td class = "entry"><p>stiffness matrix multiplier for viscous damping</p>
                      <p>(input in <span class = "ph">ANSYS®</span> using the BETAD command)</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow></msub></mrow></math></span>=</td>
<td class = "entry"><p>variable stiffness matrix multiplier for structural damping <span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">(</mo><mn class = "- topic/foreign ">2</mn><mo class = "- topic/foreign ">/</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mo class = "- topic/foreign ">)</mo><mi class = "- topic/foreign ">ξ</mi></mrow></math></span></p>
                      <p>Important note: for modal superposition is DMPRAT modal damping and therefore NOT allowed.</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">m</mi></mrow></msubsup></mrow></math></span>=</td>
<td class = "entry"><p>stiffness matrix multiplier for material j for viscous damping</p>
                      <p>(input as a material property using the DAMP label on the MP command)</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">N</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">m</mi></mrow></msub></mrow></math></span>=</td>
<td class = "entry"><p>is the number of materials with DAMP</p>
<div class = "note"><span class = "run-in.note">Note:
			</span><span class = "notecontent">this number should include all elements in the design
domain and in the manufacturing constraints.</span></div>
</td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ξ</mi></mrow></msubsup></mrow></math></span>=</td>
<td class = "entry"><p>stiffness matrix coefficient for material j for structural damping </p>
                      <p>(input as DMPR on MP command)</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">C</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub></mrow></math></span>=</td>
<td class = "entry"><p>element damping matrices in general form (are always permissible)</p></td>
</tr>
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">C</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ξ</mi></mrow></msub></mrow></math></span>=</td>
<td class = "entry"><p>eigenfrequency dependent damping matrix</p>
<div class = "note"><span class = "run-in.note">Note:
			</span><span class = "notecontent">not supported, damping defined through MDAMP is prohibited</span></div>
</td>
</tr>
</tbody></table>

<p>
Allowable viscous damping for design elements in
<span class = "ph">ANSYS®</span>:
<br/><img class = "image" id = "tso-c-usr-solver-ansys-freqspec__image_ECC992ED83E14ECA95B5E3468E3A44E3" src = "../TsoUserImages/dump_1003.png" height = "113"/><br/>
Allowable structural damping for design elements in
<span class = "ph">ANSYS®</span>:
<br/><img class = "image" id = "tso-c-usr-solver-ansys-freqspec__image_58B7DB15E3C5455C99BFFE2205D67D4F" src = "../TsoUserImages/dump_1004.png" height = "94"/><br/>
</p>
</div>

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