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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>Maximize Band Gaps </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">This section describes the setup used to avoid frequencies within certain bands.</span>

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<p><span class = "ph">SIMULIA Tosca Structure</span>
avoids problematic eigenfrequencies in dynamic problems with a special MINMAX formulation.
Here, the object function
<span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Φ</mi></mrow></math></span>
for eigenfrequencies by <span class = "ph">TARGET= MINMAX</span> is given:</p>
<table class = "table"><caption/><colgroup><col style = "width:100%"/></colgroup><tbody class = "tbody">
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<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">Φ</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">f</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub><mo class = "- topic/foreign ">-</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">f</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">*</mi></mrow></msubsup></mrow></mfrac></mrow><mo class = "- topic/foreign ">|</mo></mrow></mrow></math></span></td>
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<p>By minimizing this expression, the eigenfrequencies f will be moved away from the value of 
<span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">f</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub><mo class = "- topic/foreign ">*</mo></mrow></math></span>.
With <span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow></math></span> 
as a constant, the <span class = "ph">SIMULIA Tosca Structure</span> commands are:</p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
 ID_NAME  = dresp_eig_1
 DEF_TYPE = SYSTEM
 TYPE     = DYN_FREQ
 LC_SET   = Modal,All,1
END_

...

DRESP
 ID_NAME  = dresp_eig_20
 DEF_TYPE = SYSTEM
 TYPE     = DYN_FREQ
 LC_SET   = Modal,All,20
END_

OBJ_FUNC
 ID_NAME =  move_dresp_eig_from_15Hz
 DRESP   = dresp_eig_1, 1.0, 15.
 ...
 DRESP   = dresp_eig_20, 1.0, 15.
 TARGET  = MINMAX
END_
</code>
</pre>
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<td class = "entry"><br/><img class = "image" id = "tso-c-usr-beadSensEvOpt-beadMaxBandGaps__image_11A02B8B212147D4ADDE9E5E2A62B21C" src = "../TsoUserImages/bead_eigenvalues_convergence.png" width = "382" height = "271"/><br/></td>
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<td class = "entry">Convergence of eigenvalues of a bandgap optimization (15 Hz)</td></tr>
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<p>The second eigenmode will be pushed away from 15.0 Hz. The weighting of the design response is 1.0.</p>
<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent">Flat structures should first have the eigenvalues maximized before doing
the band-gap optimization because the optimizer must also be able to
move some eigenvalues down.</span></td></tr></table>
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