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      <title>FLUTTER</title>
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      <div class="title_refTopic" id="xps10_pagetitle">FLUTTER </div>
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      <h4 class="refClassification">Aerodynamic Flutter Data </h4>
      <p class="para_refTopic">Defines data needed to perform flutter analysis. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
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               <col span="1" width="1114*">
               <col span="1" width="984*">
               <col span="1" width="997*">
               <col span="1" width="984*">
               <col span="1" width="984*">
               <col span="1" width="984*">
               <col span="1" width="984*">
               <col span="1" width="997*">
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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>
                  </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>
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            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1">
                     <p class="para_td">FLUTTER </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">METHOD </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">DENS </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MACH </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">RFREQ </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">IMETH </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">NVALUE </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">EPS </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="1088*">
               <col span="1" width="987*">
               <col span="1" width="1000*">
               <col span="1" width="987*">
               <col span="1" width="987*">
               <col span="1" width="987*">
               <col span="1" width="987*">
               <col span="1" width="1000*">
               <col span="1" width="987*">
               <col span="1" width="987*">
            </colgroup>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1">
                     <p class="para_td">FLUTTER </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">19 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">K </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">119 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">219 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">319 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">S </p>
                  </td>
                  <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">1.-4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
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      <div class="title_refCategory">Fields:</div>
      <div class="refCategoryContent">
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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">METHOD </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Flutter analysis method.  (Character: &ldquo;K&rdquo; for K-method, &ldquo;PK&rdquo; for PK method, &ldquo;PKNL&rdquo; for PK method with no looping, &ldquo;KE&rdquo; for the K-method restricted for efficiency.) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">DENS </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Identification number of an FLFACT entry specifying density ratios to be used in flutter analysis.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MACH </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Identification number of an FLFACT entry specifying Mach numbers (<em>m</em>) to be used in flutter analysis.  (Integer &gt; 0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">RFREQ (or VEL) </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Identification number of an FLFACT entry specifying reduced frequencies (<em>k</em>) to be used in flutter analysis; for the PK and PKNL method, the velocities FLFACT entry is specified in this field.  (Integer &gt; 0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">IMETH </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Choice of interpolation method for aerodynamic matrix interpolation.  Used in the &ldquo;K&rdquo; and &ldquo;KE&rdquo; methods only.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/16topic_6.html#refVHiHi310lori');return(false);">9-6. </a> (Character:  &ldquo;L&rdquo; = linear, &ldquo;S&rdquo; = surface; Default = &ldquo;L&rdquo;.) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NVALUE </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Number of eigenvalues beginning with the first eigenvalue for output and plots.  [Integer &gt; 0; Default is the number of modal degrees-of-freedom (u<sub class="subscript">h</sub>)] 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">EPS </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Convergence parameter for k.  Used in the PK and PKNL methods only.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/16topic_6.html#refCS8bp5elori');return(false);">9-4. </a> (Real &gt; 0.0; Default = 10<sup class="superscript">−3</sup>) 
                     </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">The FLUTTER entry must be selected with the Case Control command METHOD = SID. </p>
            </li>
            <li>
               <p class="para_item">The density is given by DENS · RHOREF, where RHOREF is the reference value specified on the AERO entry and DENS is the density ratio specified on the FLFACT entry. </p>
            </li>
            <li>
               <p class="para_item">The reduced frequency is given by <em>k</em> = (<em>REFC</em> · &omega;/2 · <em>V</em>), where REFC is given on the AERO entry, &omega; is the circular frequency, and <em>V</em> is the velocity.  If <em>k</em>= 0.0, as specified on the FLFACT entry, then only the K-method may be specified and the Inverse Power method of eigenvalue extraction (INV on the EIGC entry) must be used.  Aeroelastic divergence analysis is more appropriately performed using the PK-method or PKNL method. 
               </p>
            </li>
            <li><a name="refCS8bp5elori"></a><p class="para_item"> An eigenvalue is accepted in the PK and PKNL methods when: </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkfgil-equ03.gif" border="0"></p>
               <p class="para_item"><img align="bottom" src="graphics/bulkfgil-equ04.gif" border="0"></p>
            </li>
            <li>
               <p class="para_item">When the PK or PKNL method is selected, physical displacements will only be generated for the velocities on the FLFACT that are specified as negative values of the requested velocity.  Also, structural damping as specified on the GE field of MATi entries is ignored. </p>
            </li>
            <li><a name="refVHiHi310lori"></a><p class="para_item"> If IMETH = &ldquo;L&rdquo;, a linear interpolation is performed on reduced frequencies at the Mach numbers specified on the FLFACT entry using the MKAEROi entry Mach number that is closest to the FLFACT entry Mach number.  For IMETH = &ldquo;S&rdquo;, a surface interpolation is performed across Mach numbers and reduced frequencies.  For METHOD = &ldquo;PK&rdquo; or &ldquo;PKNL&rdquo;, linear interpolation is always performed. </p>
            </li>
            <li>
               <p class="para_item">For the &ldquo;K&rdquo;, &ldquo;KE&rdquo; and &ldquo;PK&rdquo; methods, all combinations of the FLFACT entry are analyzed.  For the &ldquo;PKNL&rdquo; method, only ordered pairs are analyzed; i.e., (<em>M</em><sub class="subscript">1</sub>, <em>V</em><sub class="subscript">1</sub>), (<em>M</em><sub class="subscript">2</sub>, <em>V</em><sub class="subscript">2</sub>)...(<em>M<sub class="subscript">n</sub></em>, <em>V<sub class="subscript">n</sub></em>).  For the PKNL method, equal number of densities, Mach numbers and velocities must be specified. 
               </p>
            </li>
            <li>
               <p class="para_item">Only the &ldquo;PK&rdquo; and &ldquo;PKNL&rdquo; methods are supported for design sensitivity and optimization. </p>
            </li>
         </ol>
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