A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams

<table class="table-group" id="tab11"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2"> </td><td class="align_left" rowspan="2">Beam</td><td class="align_center" colspan="5">Modes</td></tr><tr class="thead"><td class="align_center">1</td><td class="align_center">3</td><td class="align_center">5</td><td class="align_center">7</td><td class="align_center">9</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left" rowspan="3"><span style="width: 102.421ptpx;"><svg height="20.0707pt" id="M292" style="vertical-align:-5.726pt" version="1.1" viewbox="-0.0498162 -14.3447 102.421 20.0707" width="102.421pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g 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606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.013,0,0,-0.013,97.708,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td><td class="align_center">(a)</td><td class="align_center">53.2</td><td class="align_center">16.6</td><td class="align_center">8.42</td><td class="align_center">11.4</td><td class="align_center">10.1</td></tr><tr><td class="align_center">(b)</td><td class="align_center">52.5</td><td class="align_center">18.1</td><td class="align_center">8.92</td><td class="align_center">9.82</td><td class="align_center">10.5</td></tr><tr><td class="align_center">(c)</td><td class="align_center">52.7</td><td class="align_center">17.2</td><td class="align_center">8.75</td><td class="align_center">10.3</td><td class="align_center">10.9</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Percentage of generalized forces exciting the first five symmetric modes of three types of beams excited by a uniformly distributed force over an interval of [0.4, 0.6].</div>

Shock and Vibration

tab11

Table 11

Table 11: A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams 