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      <title>FREQ5</title>
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      <div class="title_refTopic" id="xps10_pagetitle">FREQ5 </div>
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      <h4 class="refClassification">Frequency List, Alternate Form 5 </h4>
      <p class="para_refTopic">Defines a set of frequencies used in the solution of modal frequency-response problems by specification of a frequency range and fractions of the natural frequencies within that range. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10*">
               <col span="1" width="10*">
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            <thead>
               <tr>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">1 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">2 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">3 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">4 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">5 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">6 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">7 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">8 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">9 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">10 </p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">FREQ5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">SID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">F1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">F2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">FR1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">FR2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">FR3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">FR4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">FR5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">FR6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">FR7 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">-etc.- </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Example: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
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            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">FREQ5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">20.0 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">200.0 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1.0 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.8 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.9 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.95 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1.05 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1.1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1.2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Fields:</div>
      <div class="refCategoryContent">
         <table cellpadding="9" width="100%" align="center">
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               <col span="1" width="84*">
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                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Field </b></p>
                  </th>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Contents </b></p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">SID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Set identification number.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">F1 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Lower bound of frequency range in cycles per unit time.  (Real &ge; 0.0; Default = 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">F2 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Upper bound of frequency range in cycles per unit time.  (Real &gt; 0.0, F2 &gt; F1, Default = 1.0E20) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">FRi </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Fractions of the natural frequencies in the range F1 to F2.  (Real &gt;  0.0) </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Remarks: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">FREQ5 applies only to modal frequency-response solutions (SOLs 11, 111, 146, and 200) and is ignored in direct frequency response solutions. </p>
            </li>
            <li>
               <p class="para_item">FREQ5 entries must be selected with the Case Control command FREQUENCY=SID. </p>
            </li>
            <li>
               <p class="para_item">The frequencies defined by this entry are given by </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkfgil-equ16.gif" border="0"></p>
               <p class="para_item">where <em>f<sub class="subscript">N</sub><sub class="subscript">i</sub></em> are the natural frequencies in the range F1 through F2. 
               </p>
            </li>
            <li>
               <p class="para_item">In the example above, the list of frequencies will be 0.6,  0.8,  0.9,  0.95,  1.0,  1.05,  1.1, and 1.2 times each natural frequency between 20 and 2000.  If this computation results in excitation frequencies less then F1 and greater than F2, those computed excitation frequencies are ignored. </p>
               <p class="para_item">Excitation frequencies may be based on natural frequencies that are not within the range (F1 and F2) as long as the calculated excitation frequencies are within the range.  Similarly, an excitation frequency calculated based on natural frequencies within the range (F1 through F2) may be excluded if it falls outside the range. </p>
            </li>
            <li>
               <p class="para_item">Since the forcing frequencies are near structural resonances, it is important that some amount of damping be specified. </p>
            </li>
            <li>
               <p class="para_item">All FREQi entries with the same set identification numbers will be used.  Duplicate frequencies will be ignored. <em>f<sub class="subscript">N</sub></em> and <em>f</em><sub class="subscript"><em>N</em>−1</sub> are considered duplicated if 
               </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkfgil-equ17.gif" border="0"></p>
               <p class="para_item">where DFREQ is a user parameter with a default of 10<sup class="superscript">−5</sup>.  The values <em>f<sub class="subscript">MAX</sub></em> and <em>f<sub class="subscript">MIN</sub></em> are the maximum and minimum excitation frequencies of the combined FREQi entries. 
               </p>
            </li>
            <li>
               <p class="para_item">In design optimization (SOL 200), the excitation frequencies are derived from the natural frequencies computed at each design cycle. </p>
            </li>
            <li>
               <p class="para_item">In modal analysis, solutions for modal DOFs from rigid body modes at zero excitation frequencies may be discarded.  Solutions for nonzero modes are retained. </p>
            </li>
         </ol>
      </div>
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