Maintaining Specific Natural Frequency of Damped System despite Mass Modification

<table class="table-group" id="tab7"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Methods</td><td class="align_center" rowspan="2">Spring coefficient</td><td class="align_center" colspan="5">Natural frequencies (Hz)</td></tr><tr class="thead"><td class="align_center">1</td><td class="align_center">2</td><td class="align_center">3</td><td class="align_center">4</td><td class="align_center">5</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">Original</td><td class="align_left"> </td><td class="align_center"><b>38.68</b></td><td class="align_center">78.87</td><td class="align_center">117.16</td><td class="align_center">175.71</td><td class="align_center">195.51</td></tr><tr><td class="align_left">Optimal selection method</td><td class="align_center"><span style="width: 102.195ptpx;"><svg height="17.6084pt" id="M176" style="vertical-align:-6.017pt" version="1.1" 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(8.91%)</td><td class="align_center">177.30 (9.31%)</td></tr><tr><td class="align_left">Absolute value method</td><td class="align_center"><span style="width: 102.094ptpx;"><svg height="16.9233pt" id="M177" style="vertical-align:-5.3319pt" version="1.1" viewbox="-0.0498162 -11.5914 102.094 16.9233" width="102.094pt" 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="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"></path></g><g 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transform="matrix(.013,0,0,-0.013,90.6,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,96.84,-5.741)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z"></path></g></svg></span></td><td class="align_center"><b>38.65</b> (0.06%)</td><td class="align_center">76.40 (3.13%)</td><td class="align_center">106.57 (9.03%)</td><td class="align_center">160.09 (8.89%)</td><td class="align_center">177.31 (9.30%)</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Necessary spring coefficient (N/m) and the natural frequencies.</div>

International Journal of Aerospace Engineering

tab7

Table 7

Table 7: Maintaining Specific Natural Frequency of Damped System despite Mass Modification 