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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 Band Gap</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">
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.
</span>

</p>
<p>This task shows you how to:
					</p><ul><li><a href = "#tso-t-user-TopOpt-MaxBandGap-DefObjgui" id = "toc_rg" title = "">
Define an Objective Function for a Band Gap Maximization in <span class = "ph">Tosca Structure.gui</span>
</a></li></ul>
</p></td></tr></table></td></tr></table>



<div class = "body taskbody">
<div class = "section context"><p class = "context"><span class = "run-in.context">Context: </span>
<p>
In the following optimization definition, the structure should be
designed so that the first four eigenfrequencies are as far away as possible
from 150 Hz  in order to avoid the resonance at this frequency.
</p>
<p>
This is done by defining the first four eigenfrequencies as single
design responses with <span class = "ph uicontrol">TYPE = DYN_FREQ</span> and applying the
eigenfrequencies in the objective function using a min-max-formulation
as follows:
</p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
  ID_NAME  = eigenfrequency_1
  DEF_TYPE = SYSTEM
  TYPE     = DYN_FREQ
  LC_SET   = MODAL, ALL, 1
END_
  
DRESP
  ID_NAME  = eigenfrequency_2
  DEF_TYPE = SYSTEM
  TYPE     = DYN_FREQ
  LC_SET   = MODAL, ALL, 2
END_
  
DRESP
  ID_NAME  = eigenfrequency_3
  DEF_TYPE = SYSTEM
  TYPE     = DYN_FREQ
  LC_SET   = MODAL, ALL, 3
END_
  
DRESP
  ID_NAME  = eigenfrequency_4
  DEF_TYPE = SYSTEM
  TYPE     = DYN_FREQ
  LC_SET   = MODAL, ALL, 4
END_
  
OBJ_FUNC
  DRESP    = eigenfrequency_1, 1.0, 150.0
  DRESP    = eigenfrequency_2, 1.0, 150.0
  DRESP    = eigenfrequency_3, 1.0, 150.0
  DRESP    = eigenfrequency_4, 1.0, 150.0
  TARGET   = MINMAX
END_
</code>
</pre>
</p></div>

</div>


<article class = "topic task nested1" aria-labelledby = "ariaid-title2" id = "tso-t-user-TopOpt-MaxBandGap-DefObjgui">
<h2 class = "title topictitle2">
Define an Objective Function for a Band Gap Maximization in <span class = "ph">Tosca Structure.gui</span>
</h2>

<div class = "body taskbody">
<section><ol class = "ol steps"><li class = "li step">

Create four design responses: Choose <span class = "ph uicontrol">Command &gt; DRESP</span>.

</li><li class = "li step">

Set <span class = "ph uicontrol">DefType = System</span>, <span class = "ph uicontrol">
Category
= Base
</span> and <span class = "ph uicontrol">Type = DYN_FREQ</span>.

</li><li class = "li step">

Choose the <span class = "ph">load cases</span>
by pressing the <span class = "ph uicontrol">Add LC</span> button and setting Analysis Type to <span class = "ph uicontrol">MODAL</span>,
entering the <span class = "ph">load case</span>
ID and the numbers of eigenmodes (1 for the first term, 2 for the second
one, etc.) in the <span class = "ph uicontrol">Eigenmode/Subcase</span> field.
<br/><img class = "image" src = "../TsoUserImages/topo_dresp_eigenfreq_dialog_5.png" width = "450"/><br/>

</li><li class = "li step">

When the design responses are defined, create an <span class = "ph uicontrol">OBJ_FUNC</span> and choose the design responses and their reference values (set
<span class = "ph uicontrol">RefValue = 150</span> for each design response).

</li></ol></section>
</div>

</article>


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