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      <title>FREQ3</title>
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      <div class="title_refTopic" id="xps10_pagetitle">FREQ3 </div>
      <hr noshade="true">
      <h4 class="refClassification">Frequency List, Alternate 3 </h4>
      <p class="para_refTopic">Defines a set of excitation frequencies for modal frequency-response solutions by specifying number of excitation frequencies between two modal frequencies. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="9.96*">
               <col span="1" width="9.96*">
               <col span="1" width="9.96*">
               <col span="1" width="9.96*">
               <col span="1" width="9.96*">
               <col span="1" width="9.96*">
               <col span="1" width="10.90*">
               <col span="1" width="9.96*">
               <col span="1" width="9.40*">
               <col span="1" width="9.96*">
            </colgroup>
            <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">FREQ3 </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">TYPE </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">NEF </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CLUSTER </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" 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*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
            </colgroup>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">FREQ3 </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">LINEAR </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">10 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">2.0 </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">
            <colgroup span="1">
               <col span="1" width="16*">
               <col span="1" width="84*">
            </colgroup>
            <thead>
               <tr>
                  <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 modal frequency range in cycles per unit time.  (Real &ge; 0.0 for TYPE = LINEAR and Real = 0.0 for TYPE = LOG) </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 modal frequency range in cycles per unit time.  (Real &gt; 0.0, F2 &ge; F1, Default = F1) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">TYPE </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">LINEAR or LOG.  Specifies linear or logarithmic interpolation between frequencies.  (Character; Default = &ldquo;LINEAR&rdquo;) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NEF </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Number of excitation frequencies within each subrange including the end points.  The first subrange is between F1 and the first modal frequency within the bounds.  The second subrange is between first and second modal frequencies between the bounds.  The last subrange is between the last modal frequency within the bounds and F2.  (Integer &gt; 1, Default = 10) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">CLUSTER </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Specifies clustering of the excitation frequency near the end points of the range.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/16topic_15.html#refvxjGoe4lori');return(false);">21-6. </a> (Real &gt; 0.0; Default = 1.0) 
                     </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">FREQ3 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">FREQ3 entries must be selected with the Case Control command FREQUENCY = SID. </p>
            </li>
            <li>
               <p class="para_item">In the example above, there will be 10 frequencies in the interval between each set of modes within the bounds 20 and 2000, plus 10 frequencies between 20 and the lowest mode in the range, plus 10 frequencies between the highest mode in the range and 2000. </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-equ13.gif" border="0"></p>
               <p class="para_item">where DFREQ is a user parameter, with a default of 10<sup class="superscript">−5</sup>. <em>f<sub class="subscript">MAX</sub></em>  an <em>f<sub class="subscript">MIN</sub></em> are the maximum and minimum excitation frequencies of the combined FREQi entries. 
               </p>
            </li>
            <li><a name="refvxjGoe4lori"></a><p class="para_item">CLUSTER is used to obtain better resolution near the modal frequencies where the response varies the most.  CLUSTER &gt; 1.0 provides closer spacing of excitation frequency towards the ends of the frequency range, while values of less than 1.0 provide closer spacing towards the center of the frequency range.  For example, if the frequency range is between 10 and 20, NEF = 11, TYPE = &ldquo;LINEAR&rdquo;; then, the excitation frequencies for various values of CLUSTER would be as shown in <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/16topic_15.html#ref92642');return(false);">Table 15-1</a>. 
               </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkfgil-equ14.gif" border="0"></p>
               <p class="para_item">where </p>
               <table cellpadding="9" width="100%" align="center">
                  <colgroup span="1">
                     <col align="center" span="1" width="11*">
                     <col span="1" width="83*">
                  </colgroup>
                  <tbody>
                     <tr>
                        <td colspan="1" rowspan="1" valign="top">
                           <p class="para_td">&xi; </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">= −1 + 2(<em>k</em>−1)/ (NEF−1) is a parametric coordinate between -1 and 1 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td colspan="1" rowspan="1" valign="top">
                           <p class="para_td">k </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">= varies from 1 to NEF (<em>k</em> = 1, 2, ..., NEF) 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td colspan="1" rowspan="1" valign="top">
                           <p class="para_td"><img align="bottom" src="graphics/bulkfgil-ufig04.gif" border="0"></p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">= is the lower limit of the frequency subrange </p>
                        </td>
                     </tr>
                     <tr>
                        <td colspan="1" rowspan="1" valign="top">
                           <p class="para_td"><img align="bottom" src="graphics/bulkfgil-ufig05.gif" border="0"></p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">= is the upper limit o the subrange </p>
                        </td>
                     </tr>
                     <tr>
                        <td colspan="1" rowspan="1" valign="top">
                           <p class="para_td"><img align="bottom" src="graphics/bulkfgil-ufig06.gif" border="0"></p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">= is the k-th excitation frequency </p>
                        </td>
                     </tr>
                     <tr>
                        <td colspan="1" rowspan="1" valign="top">
                           <p class="para_td"><img align="bottom" src="graphics/bulkfgil-ufig07.gif" border="0"></p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">= is the frequency, or the logarithm of the frequency, depending on the value specified for TYPE </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br><a name="ref92642"></a><div class="title_tableWrapper">Table 15-1. CLUSTER Usage Example </div>
               <table border="1" cellpadding="6" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="20.13*">
                     <col span="1" width="9.98*">
                     <col span="1" width="15.47*">
                     <col span="1" width="15.47*">
                     <col span="1" width="12.98*">
                     <col span="1" width="12.98*">
                     <col span="1" width="12.98*">
                  </colgroup>
                  <thead>
                     <tr bgcolor="#E0E0E0">
                        <th align="center" colspan="1" rowspan="3">
                           <p class="para_th">Excitation Frequency Number </p>
                        </th>
                        <th align="center" colspan="1" rowspan="3">
                           <p class="para_th">&xi; </p>
                        </th>
                        <th align="center" colspan="5" rowspan="1">
                           <p class="para_th">CLUSTER</p>
                        </th>
                     </tr>
                     <tr bgcolor="#E0E0E0">
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th">c=0.25 </p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th">c-0.50 </p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th">c-1.0 </p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th">c-2.0 </p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th">c-4.0 </p>
                        </th>
                     </tr>
                     <tr>
                        <th align="center" bgcolor="#E0E0E0" colspan="5" rowspan="1">
                           <p class="para_th">Excitation Frequencies in Hertz </p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1 </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">10.00 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">10.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">10.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">10.00 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">10.00 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">2 </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">12.95 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">11.8 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">11.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">10.53 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">10.27 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">3 </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">14.35 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">13.2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">12.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">11.13 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">10.60 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">4 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">-0.4 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">14.87 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">14.2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">13.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">11.84 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">11.02 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">5 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">-0.2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">14.99 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">14.8 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">14.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">12.76 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">11.66 </p>
                        </td>
                     </tr>
                     <tr>
                        <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">0.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">15.00 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">15.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">15.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">15.00 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">15.00 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">7 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">0.2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">15.01 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">15.2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">16.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">17.24 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">18.34 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">8 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">0.4 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">15.13 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">15.8 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">17.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">18.16 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">18.98 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">9 </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">15.65 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">16.8 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">18.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">18.87 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">19.40 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">10 </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">17.05 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">18.2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">19.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">19.47 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">19.73 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">11 </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">20.00 </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">20.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">20.00 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">20.00 </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br></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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