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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>Sizing Optimization for NVH Analyses</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"> This section describes the various supported finite element types and the available design responses for modal and acoustic optimization.</span>
</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-sizing-nvh-optimization__tso-c-usr-sizing-nvh-dresp" id = "toc_rg" title = "">Types of Supported Design Responses</a></li><li><a href = "#tso-c-usr-sizing-nvh-optimization__tso-c-usr-sizing-nvh-drespmath" id = "toc_rg" title = "">Relations for Calculation of Design Responses from Fundamental Quantities</a></li><li><a href = "#tso-c-usr-sizing-nvh-optimization__tso-c-usr-sizing-nvh-damping" id = "toc_rg" title = "">Importance of Specifying Damping Parameters</a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">

<div class = "section" id = "tso-c-usr-sizing-nvh-optimization__tso-c-usr-sizing-nvh-dresp"><h2 class = "title sectiontitle">Types of Supported Design Responses</h2>

<p>All the <code class = "ph codeph">DRESP</code> quantities are <span class = "ph">load case</span> dependent. </p>
<p>N implies <code class = "ph codeph">DRESP</code> is calculated at the node, and thus a single node or group of nodes must be specified. </p>
<p>E implies <code class = "ph codeph">DRESP</code> is calculated for the element; thus, a single element or a group of elements are specified. </p>
<table class = "table" id = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E"><caption/><colgroup><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> Name of design response </th>
<th class = "entry" id = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> Selection area </th>
<th class = "entry" id = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3">Description </th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_ACCEL_X </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Acceleration in x-direction for frequency response. </td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_ACCEL_Y </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Acceleration in y-direction for frequency response. </td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"><code class = "ph codeph"> FS_ACCEL_Z </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Acceleration in z-direction for frequency response. </td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_COMP </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> E </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Dynamic compliance for frequency response.</td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_DBA_PRESSURE </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Sound Pressure Level [dBA]. </td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"><code class = "ph codeph">FS_DB_PRESSURE </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Sound Pressure Level [dB]. </td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_DISP_ABS </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Absolute amplitude for frequency response.</td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_DISP_X_ABS </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Amplitude in x-direction for frequency Response. </td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_DISP_Y_ABS </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Amplitude in z-direction for frequency response. </td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_DISP_Z_ABS </code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2"> N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Amplitude in z-direction for frequency response. </td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_PHASE_X</code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2">N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Phase in x-direction for frequency response.</td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"><code class = "ph codeph">FS_PHASE_Y</code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2">N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Phase in Y-direction for frequency response.</td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"><code class = "ph codeph">FS_PHASE_Z</code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2">N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Phase in Z-direction for frequency response.</td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_PRESSURE_X</code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2">N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Instantaneous sound pressure [Pa].</td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_RMS_PRESSURE</code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2">N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Effective sound pressure (RMS) [Pa].</td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_VELOCITY_X</code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2">N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Velocity in x-direction for frequency response.</td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_VELOCITY_Y</code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2">N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Velocity in y-direction for frequency response.</td>
</tr>
<tr class = "row valign-middle">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__1"> <code class = "ph codeph">FS_VELOCITY_Z</code></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__2">N </td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_6E28A34A21F649D79597ADB93A12C68E__entry__3"> Velocity in z-direction for frequency response.</td>
</tr>
</tbody></table>
</div>


<div class = "section" id = "tso-c-usr-sizing-nvh-optimization__tso-c-usr-sizing-nvh-drespmath"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Relations for Calculation of Design Responses from Fundamental Quantities</h2>


<table class = "table" id = "tso-c-usr-sizing-nvh-optimization__table_805D18F78C5A4794A9C13345F11FE35E"><caption/><colgroup><col/><col/></colgroup><tbody class = "tbody">

<tr class = "row">
<td class = "entry valign-middle"><code class = "ph codeph">FS_COMP</code></td>
<td class = "entry"><span class = "ph inlineequation"><math altimg-valign = "7" altimg-height = "27" altimg-width = "244" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">C</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">d</mi><mi class = "- topic/foreign ">y</mi><mi class = "- topic/foreign ">n</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">|</mo><mo class = "- topic/foreign ">{</mo><mi class = "- topic/foreign ">P</mi><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">}</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">T</mi></mrow></msubsup><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><mi class = "- topic/foreign ">u</mi><mo class = "- topic/foreign ">}</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><mo class = "- topic/foreign ">{</mo><mi class = "- topic/foreign ">P</mi><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">}</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">T</mi></mrow></msubsup><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><mi class = "- topic/foreign ">u</mi><mo class = "- topic/foreign ">}</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow></msub></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry valign-middle"><code class = "ph codeph">FS_DISP_ABS</code></td>
<td class = "entry"><span class = "ph inlineequation"><math altimg-valign = "9" altimg-height = "33" altimg-width = "331" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry valign-middle"><p><code class = "ph codeph">FS_DISP_X_ABS</code></p>
                                      <p><code class = "ph codeph">FS_DISP_Y_ABS</code></p>
                                      <p><code class = "ph codeph">FS_DISP_Z_ABS</code></p></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "8" altimg-height = "32" altimg-width = "137" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "159" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">cos</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "9" altimg-height = "33" altimg-width = "135" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "7" altimg-height = "21" altimg-width = "157" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">cos</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "8" altimg-height = "32" altimg-width = "134" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "156" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">cos</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry valign-middle"><p><code class = "ph codeph">FS_PHASE_X_ABS</code></p>
                                      <p><code class = "ph codeph">FS_PHASE_Y_ABS</code></p>
                                      <p><code class = "ph codeph">FS_PHASE_Z_ABS</code></p></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "14" altimg-height = "33" altimg-width = "118" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">a</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mi class = "- topic/foreign ">arctan</mi><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow></msub></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow></msub></mrow></mfrac></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "159" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">cos</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "15" altimg-height = "35" altimg-width = "117" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">a</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mi class = "- topic/foreign ">arctan</mi><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow></msub></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow></msub></mrow></mfrac></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "7" altimg-height = "21" altimg-width = "157" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">cos</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "14" altimg-height = "33" altimg-width = "116" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">a</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mi class = "- topic/foreign ">arctan</mi><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow></msub></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow></msub></mrow></mfrac></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "156" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">cos</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry valign-middle"><p><code class = "ph codeph">FS_ACCEL_X_ABS</code></p>
                                      <p><code class = "ph codeph">FS_ACCEL_Y_ABS</code></p>
                                      <p><code class = "ph codeph">FS_ACCEL_Z_ABS</code></p></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "8" altimg-height = "32" altimg-width = "157" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">¨</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "22" altimg-width = "175" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">¨</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">−</mo><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">¨</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">cos</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "9" altimg-height = "33" altimg-width = "154" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">¨</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "7" altimg-height = "25" altimg-width = "174" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">¨</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">−</mo><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">¨</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">cos</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "8" altimg-height = "32" altimg-width = "154" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">¨</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "22" altimg-width = "172" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">¨</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">−</mo><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">¨</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">cos</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry valign-middle"><p><code class = "ph codeph">FS_VELOCITY_X_ABS</code></p>
                                      <p><code class = "ph codeph">FS_VELOCITY_Y_ABS</code></p>
                                      <p><code class = "ph codeph">FS_VELOCITY_Z_ABS</code></p></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "8" altimg-height = "32" altimg-width = "149" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">˙</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "22" altimg-width = "172" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">˙</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">−</mo><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">˙</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">sin</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "9" altimg-height = "33" altimg-width = "146" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">˙</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "7" altimg-height = "25" altimg-width = "171" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">˙</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">−</mo><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">˙</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">sin</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "8" altimg-height = "32" altimg-width = "146" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">˙</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>,
                         so that <span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "22" altimg-width = "169" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">˙</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">−</mo><mover class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">˙</mo></mrow></mover></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">⁢</mo><mtext class = "- topic/foreign "> </mtext><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">sin</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mi class = "- topic/foreign ">t</mi><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></math></span></p></td>
</tr>
<tr class = "row">
<td class = "entry valign-middle"><code class = "ph codeph">FS_PRESSURE</code></td>
<td class = "entry"><span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "13" altimg-width = "12" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry valign-middle"><code class = "ph codeph">FS_RMS_PRESSURE</code></td>
<td class = "entry"><span class = "ph inlineequation"><math altimg-valign = "18" altimg-height = "35" altimg-width = "82" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">r</mi><mi class = "- topic/foreign ">m</mi><mi class = "- topic/foreign ">s</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow><mrow class = "- topic/foreign "><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msqrt></mrow></mfrac></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry valign-middle"><code class = "ph codeph">FS_DB_PRESSURE</code></td>
<td class = "entry"><span class = "ph inlineequation"><math altimg-valign = "13" altimg-height = "37" altimg-width = "157" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">d</mi><mi class = "- topic/foreign ">B</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mn class = "- topic/foreign ">10</mn><mi class = "- topic/foreign ">log</mi><mo class = "- topic/foreign ">⁡</mo><mtext class = "- topic/foreign "> </mtext><mo class = "- topic/foreign ">(</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">r</mi><mi class = "- topic/foreign ">m</mi><mi class = "- topic/foreign ">s</mi></mrow></msub></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">0</mn></mrow></msub></mrow></mfrac><mo class = "- topic/foreign ">)</mo></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry valign-middle"><code class = "ph codeph">FS_DBA_PRESSURE</code></td>
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "13" altimg-height = "37" altimg-width = "166" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">d</mi><mi class = "- topic/foreign ">B</mi><mi class = "- topic/foreign ">A</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mn class = "- topic/foreign ">20</mn><mi class = "- topic/foreign ">log</mi><mo class = "- topic/foreign ">⁡</mo><mtext class = "- topic/foreign "> </mtext><mo class = "- topic/foreign ">(</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">r</mi><mi class = "- topic/foreign ">m</mi><mi class = "- topic/foreign ">s</mi></mrow></msub></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">p</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">0</mn></mrow></msub></mrow></mfrac><mo class = "- topic/foreign ">)</mo></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "28" altimg-height = "67" altimg-width = "335" class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mtext class = "- topic/foreign "> </mtext><mn class = "- topic/foreign ">10</mn><mi class = "- topic/foreign ">log</mi><mo class = "- topic/foreign ">⁡</mo><mtext class = "- topic/foreign "> </mtext><mo class = "- topic/foreign ">(</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1.562339</mn><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">4</mn></mrow></msup></mrow><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">107.65265</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">)</mo><mrow class = "- topic/foreign "><mtext class = "- topic/foreign "> </mtext><mo class = "- topic/foreign ">(</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">737.86223</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">)</mo></mrow></mrow></mrow></mfrac><mo class = "- topic/foreign ">)</mo></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "38" altimg-height = "86" altimg-width = "343" class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mtext class = "- topic/foreign "> </mtext><mn class = "- topic/foreign ">10</mn><mi class = "- topic/foreign ">log</mi><mo class = "- topic/foreign ">⁡</mo><mtext class = "- topic/foreign "> </mtext><mo class = "- topic/foreign ">(</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2.242881</mn><mo class = "- topic/foreign ">⁢</mo><mo class = "- topic/foreign ">⋅</mo><mtext class = "- topic/foreign "> </mtext><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">10</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">16</mn></mrow></msup><mtext class = "- topic/foreign "> </mtext><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">4</mn></mrow></msup></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">20.598997</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mrow class = "- topic/foreign "><mtext class = "- topic/foreign "> </mtext><mo class = "- topic/foreign ">(</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">12194.22</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></mrow></mfrac><mo class = "- topic/foreign ">)</mo></mrow></math></span></p></td>
</tr>
</tbody></table>
</div>


<div class = "section" id = "tso-c-usr-sizing-nvh-optimization__tso-c-usr-sizing-nvh-damping"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Importance of Specifying Damping Parameters</h2>

<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><p>
<ul class = "ul">
<li class = "li">It is always recommended to have some kind of damping, either viscous damping or structural damping.</li>
<li class = "li">
It is recommended to have more
damping than might be present in correct physical system. The increase of
damping enforces the peaks in the spectra to be wider. Thus, the chance for
ending in a local minimum is less likely.
</li>
</ul>
</p></span></td></tr></table>

<p>
The relationship between the viscous damping
<span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "29" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">β</mi></mrow></math></span>
and the fraction of critical damping
<span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "9" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ξ</mi></mrow></math></span>
, at frequency
<span class = "ph inlineequation"><math altimg-valign = "0" altimg-height = "9" altimg-width = "12" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ω</mi></mrow></math></span>
is given by the following equation:
</p>
<table class = "table" id = "tso-c-usr-sizing-nvh-optimization__ae205879"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "9" altimg-height = "29" altimg-width = "118" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ξ</mi><mo class = "- topic/foreign ">=</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></mfrac><mo class = "- topic/foreign ">(</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ω</mi></mrow></mfrac><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">β</mi><mi class = "- topic/foreign ">ω</mi><mo class = "- topic/foreign ">)</mo></mrow></math></span></p></td>
</tr>
</tbody></table>

<p>
The critical damping indicates the switch from oscillatory response to
<span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "35" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ξ</mi><mo class = "- topic/foreign ">=</mo><mn class = "- topic/foreign ">1</mn></mrow></math></span>
nonoscillatory. For normal application the damping is around 0.5% (0.005)
to around 15% (0.15).
</p>
<p>If the damping is unknown, a recommendation is to use the following numbers for the viscous damping:</p>
<table class = "table" id = "tso-c-usr-sizing-nvh-optimization__table_CB4B6A973D1E40C583287224B6EEBA3A"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "144" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">≈</mo><mn class = "- topic/foreign ">0</mn><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">03</mn><mi class = "- topic/foreign ">ω</mi><mo class = "- topic/foreign ">≈</mo><mn class = "- topic/foreign ">0</mn><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">13</mn><mi class = "- topic/foreign ">f</mi></mrow></math></span></p>
                      <p><span class = "ph inlineequation"><math altimg-valign = "12" altimg-height = "32" altimg-width = "128" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi><mo class = "- topic/foreign ">≈</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">0</mn><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">03</mn></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ω</mi></mrow></mfrac><mo class = "- topic/foreign ">≈</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">0</mn><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">006</mn></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">f</mi></mrow></mfrac></mrow></math></span></p></td>
</tr>
</tbody></table>

<p>
The relationship between the structural damping and the fraction of critical damping
<span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "9" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ξ</mi></mrow></math></span>
at frequency
<span class = "ph inlineequation"><math altimg-valign = "0" altimg-height = "9" altimg-width = "12" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ω</mi></mrow></math></span>
is given by the following equation:
</p>
<table class = "table" id = "tso-c-usr-sizing-nvh-optimization__table_4C9FFECFFE4C439B8FAEEFDEDC17A1C1"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p><span class = "ph inlineequation"><math altimg-valign = "15" altimg-height = "41" altimg-width = "130" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ξ</mi><mo class = "- topic/foreign ">=</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></mfrac><mo class = "- topic/foreign ">(</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow></msub></mrow><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ω</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></mfrac><mo class = "- topic/foreign ">+</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></math></span></p></td>
</tr>
</tbody></table>

<p>
Stiffness-proportional damping more effectively damps higher modes of the domain. If the
optimization includes the first peaks in the spectrum and only structural damping is
applied, then apply a high damping (&gt;10%) for not creating too narrow peaks.
Alternatively, use more sampling points in the frequency response range, especially around
the eigenfrequencies.
</p>
<p>
<ul class = "ul">
<li class = "li">The user must always define the damping for the design elements and the elements included in the manufacturing constraints using OPT_PARAM.</li>
<li class = "li">The design elements and the elements included in the manufacturing constraints should all have the same damping.</li>
</ul>
</p>
<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><p>
<ul class = "ul">
<li class = "li">Generally, all damping appearances being independent on eigenfrequencies are allowed.</li>
<li class = "li">Damping depending on the eigenfrequencies and eigenmodes are not allowed.</li>
<li class = "li">
Consequently, modal damping is not allowed in the
finite element input file for the frequency response. All kind of discrete
damping elements and other kind of damping are allowed outside the design
domain.
</li>
<li class = "li">
During the designing the eigenfrequencies change significantly and, thus, will the modal damping
also change significantly. The damping of the elements in the design domain must
be defined in the parameter file.
</li>
</ul>
</p></span></td></tr></table>

<p>
<table class = "table" id = "tso-c-usr-sizing-nvh-optimization__table_5A099333CECD456A9E79D01804179A3B"><caption/><colgroup><col style = "width:50%"/><col style = "width:50%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-sizing-nvh-optimization__table_5A099333CECD456A9E79D01804179A3B__entry__1">Viscous Damping</th>
<th class = "entry" id = "tso-c-usr-sizing-nvh-optimization__table_5A099333CECD456A9E79D01804179A3B__entry__2">Structural Damping</th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_5A099333CECD456A9E79D01804179A3B__entry__1">
<p>
Viscous damping  for design elements (Rayleigh damping) where the
damping matrix is assumed to be proportional to the mass and the stiffness
matrices. The damping matrix is defined as
</p>
<p><span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "165" class = "- topic/foreign "><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">C</mi><mo class = "- topic/foreign ">]</mo></mrow><mo class = "- topic/foreign ">=</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">M</mi><mo class = "- topic/foreign ">]</mo><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">β</mi><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">K</mi><mo class = "- topic/foreign ">]</mo></mrow></math></span></p>
<p>
The viscous damping for the elements in the design domain should always
be defined using the OPT_PARAM command, where A stands for viscous
damping scaled with mass matrix and B stands for the viscous damping
scaled with stiffness matrix, as shown below:
</p>
<pre class = "codeblock">
<code class = "ph codeph">
OPT_PARAM
  ...
  DAMP_VISCOUS_MASS =  A
  DAMP_VISCOUS_STIFF = B
  ...
END_
</code>
</pre></td>
<td class = "entry" headers = "tso-c-usr-sizing-nvh-optimization__table_5A099333CECD456A9E79D01804179A3B__entry__2">
<p>
Structural damping  for design elements where the damping matrix is
assumed to be proportional to the mass and the stiffness matrices divided by
the excitation and defined as
</p>
<p><span class = "ph inlineequation"><math altimg-valign = "5" altimg-height = "19" altimg-width = "272" class = "- topic/foreign "><mrow class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">C</mi><mo class = "- topic/foreign ">]</mo></mrow><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow></msub><mo class = "- topic/foreign ">/</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">M</mi><mo class = "- topic/foreign ">]</mo><mo class = "- topic/foreign ">+</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">β</mi></mrow><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi></mrow></msub><mo class = "- topic/foreign ">/</mo><mi mathvariant = "normal" class = "- topic/foreign ">Ω</mi><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">[</mo><mi class = "- topic/foreign ">K</mi><mo class = "- topic/foreign ">]</mo></mrow></math></span></p>
<p>
The structural damping for the elements in the design domain should always
be defined using the OPT_PARAM commend, where A stands for structural
damping scaled with mass matrix and B stands for structural damping
scaled with stiffness matrix, like the following:
</p>
<pre class = "codeblock">
<code class = "ph codeph">
OPT_PARAM
  ...
  DAMP_STRUCTURAL_MASS =  A
  DAMP_STRUCTURAL_STIFF = B
  ...
END_
</code>
</pre>
</td>
</tr>
</tbody></table>
</p>

<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><p> Concentrated and discrete dampers (often viscous) and other types of damping elements outside the design domain are all allowed.</p></span></td></tr></table>

<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.warning">Warning:
				</span><span class = "notecontent"><p> Modal damping (also called fraction of critical damping) in all forms is prohibited.</p></span></td></tr></table>
</div>


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