Sound Attenuation of Membranes Loaded with Square Frame-Shaped Masses

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Property</td><td class="align_center">Polyetherimide (PEI)</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">Mass density (kg/m<sup>3</sup>)</td><td class="align_center">1200</td></tr><tr><td class="align_left">Young’s modulus (Pa)</td><td class="align_center"><span style="width: 46.5453ptpx;"><svg height="11.9413pt" id="M68" style="vertical-align:-0.3499002pt" version="1.1" viewbox="-0.0498162 -11.5914 46.5453 11.9413" width="46.5453pt" 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="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z" id="g113-55"></path><glyph.data 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vert-adv-y="480"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,41.424,-5.741)"><path d="M247 635C116 635 39 518 39 421C39 315 113 237 221 237C239 237 258 241 281 253L349 289C315 140 204 42 60 19L66 -15C90 -15 153 -5 207 16C344 70 447 199 447 385C447 521 373 635 247 635ZM231 598C329 598 356 478 356 390C356 371 355 347 352 325C330 309 297 297 262 297C179 297 127 369 127 456C127 515 156 598 231 598Z" id="g50-58"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></span></td></tr><tr><td class="align_left">Poisson ratio</td><td class="align_center">0.36</td></tr><tr><td class="align_left">Thickness (mm)</td><td class="align_center">0.076</td></tr><tr><td class="align_left">Length (mm)</td><td class="align_center">27.4</td></tr><tr><td class="align_left">Tension (Pa)</td><td class="align_center"><span style="width: 46.5453ptpx;"><svg height="11.9413pt" id="M69" style="vertical-align:-0.3499002pt" version="1.1" 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Physical properties of membrane material [<a href="/journals/mpe/2016/1740236/#B16">16</a>]. 

Mathematical Problems in Engineering

Sound Attenuation of Membranes Loaded with Square Frame-Shaped Masses

Table 1