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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>About Typical Optimization Tasks for Modal Analysis</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">Often the design target is to increase the first eigenfrequencies
in an eigenfrequency spectrum. It is important to consider more than
the first natural eigenfrequency when increasing the natural frequencies
using optimization. Otherwise, the first and secondary mode might switch
during the optimization as shown in the figure below. </span>

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<p>Optimizing all the lowest eigenfrequencies using the Kreisselmeier-Steinhauser formulation is demonstrated in figure (b)
and the single lowest eigenfrequency using mode tracking is shown in the figure (a):</p>
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</tbody></table><p>For some optimization problems, it can be desirable that a sudden eigenfrequency
is increased whereas the other eigenfrequencies are allowed to decrease (see figure (a)).</p>
<p><ul class = "ul"><li class = "li"><a class = "xref" href = "tso-t-user-TopOpt-ModAna-Max1Fr.htm#tso-t-user-TopOpt-ModAna-Max1Fr" title = "You can increase several lowest eigenfrequencies.">Maximizing the First Eigenfrequencies</a> describes how  several lowest eigenfrequencies
are increased (see figure (b)).</li>
<li class = "li"><a class = "xref" href = "tso-t-user-TopOpt-ModAna-MaxFr.htm#tso-t-user-TopOpt-ModAna-MaxFr" title = "You can increase a specific eigenfrequency in the eigenfrequency spectrum belonging to a certain eigenmode. In this case, a specific eigenfrequency is defined using TYPE = DYN_FREQ.">Maximizing the Eigenfrequency of a Certain Eigenmode</a> addresses how a specific eigenfrequency
in an eigenfrequency spectrum is optimized using mode tracking (see figure (a)). </li>
<li class = "li"><a class = "xref" href = "tso-t-user-TopOpt-ModAna-MaxBandGap.htm#tso-t-user-TopOpt-ModAna-MaxBandGap" title = "Sometimes it is desirable that the first eigenfrequencies are as far away as possible from a certain value. For example, if an engine mainly works at 150 Hz, there should be an as large as possible interval called a band gap around 150 Hz in the eigenfrequency spectrum containing no eigenfrequencies. You can maximize the band gap to decrease some eigenfrequencies and increase others.">Maximizing the Band Gap</a> describes
how a band gap in the eigenfrequency spectrum can be designed. A band
gap in the eigenfrequency spectrum contains no eigenfrequencies.</li><li class = "li"><a class = "xref" href = "tso-t-user-TopOpt-ConstFR.htm#tso-t-user-TopOpt-ConstFR" title = "You can define constraints for eigenfrequencies in the topology optimization tasks such as stiffness optimization or minimizing the mass.">Constraining an Eigenfrequency</a> shows how an eigenfrequency can be applied in a constraint, for example,
	when maximizing the stiffness under the condition that the first eigenfrequency
	is above 100 Hz or when minimizing the mass under the condition that
	the eigenfrequencies are  below or above certain specified values.</li></ul></p>




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