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      <title>FREQ4</title>
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      <div class="title_refTopic" id="xps10_pagetitle">FREQ4 </div>
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      <h4 class="refClassification">Frequency List, Alternate Form 4 </h4>
      <p class="para_refTopic">Defines a set of frequencies used in the solution of modal frequency-response problems by specifying the amount of &ldquo;spread&rdquo; around each natural frequency and the number of equally spaced excitation frequencies within the spread. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
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                  <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>
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                     <p class="para_th">4 </p>
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                     <p class="para_th">5 </p>
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                     <p class="para_th">6 </p>
                  </th>
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                     <p class="para_th">7 </p>
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                     <p class="para_th">8 </p>
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                     <p class="para_th">9 </p>
                  </th>
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                     <p class="para_th">10 </p>
                  </th>
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            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">FREQ4 </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">FSPD </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">NFM </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>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
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         </table><br></div>
      <div class="title_refCategory">Example: </div>
      <div class="refCategoryContent">
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            <tbody>
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                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">FREQ4 </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">0.30 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">21 </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">
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                     <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>
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                  <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>
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                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">FSPD </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Frequency spread, +/- the fractional amount specified for each mode which occurs in the frequency range F1 to F2.  (1.0 &gt; Real &gt; 0.0, Default = 0.10) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NFM </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Number of evenly spaced frequencies per &ldquo;spread&rdquo; mode.  (Integer &gt; 0; Default = 3; If NFM is even, NFM + 1 will be used.) </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">FREQ4 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">FREQ4 entries must be selected with the Case Control command FREQUENCY=SID. </p>
            </li>
            <li>
               <p class="para_item">There will be NFM excitation frequencies between (1−<em>FSPD</em>) <em>f<sub class="subscript">N</sub></em> and (1+<em>FSPD</em>) <em>f<sub class="subscript">N</sub></em>, for each natural frequency in the range F1 to F2. 
               </p>
            </li>
            <li>
               <p class="para_item">In the example above there will be 21 equally spaced frequencies across a frequency band of 0.7 · <em>f<sub class="subscript">N</sub></em> to 1.3 · <em>f<sub class="subscript">N</sub></em> for each natural frequency that occurs between 20 and 2000.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/16topic_16.html#ref22933');return(false);">Figure 15-</a> for the definition of frequency spread. 
               </p><a name="ref22933"></a><div class="figure">
                  <p align="center"><img align="bottom" src="graphics/bulkfgil-fig04.gif"></p>
               </div>
               <div class="title_figure">Figure. Frequency Spread Definition </div>
               <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">The frequency spread can be used also to define the half-power bandwidth.  The half-power bandwidth is given by 2 · &xi; · <em>f<sub class="subscript">N</sub></em>, where &xi; is the damping ratio.  Therefore, if FSPD is specified equal to the damping ratio for the mode, NFM specifies the number of excitation frequency within the half-power bandwidth.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/16topic_16.html#ref45298');return(false);">Figure 15-</a> for the definition of half-power bandwidth. 
               </p><a name="ref45298"></a><div class="figure">
                  <p align="center"><img align="bottom" src="graphics/bulkfgil-fig05.gif"></p>
               </div>
               <div class="title_figure">Figure. Half-Power Bandwidth Definition </div>
            </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-equ15.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>
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