The Effect of Geometrical Parameters on Resonance Characteristics of Acoustic Metamaterials with Negative Effective Modulus

<table class="fixed-width table-group" id="tab1"><tr><td><table class="table"><colgroup><col style="width:11.52em"/><col style="width:3.22em"/><col style="width:3.14em"/><col style="width:3.25em"/><col style="width:3.19em"/><col style="width:3.24em"/></colgroup><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">The radius of neck/mm</td><td class="align_center">0.5</td><td class="align_center">1.0</td><td class="align_center">1.5</td><td class="align_center">2.0</td><td class="align_center">2.5</td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">Theoretical frequency/Hz</td><td class="align_center">2200</td><td class="align_center">3502</td><td class="align_center">4602</td><td class="align_center">5602</td><td class="align_center">6491</td></tr><tr><td class="align_left">Simulate frequency/Hz</td><td class="align_center">2190</td><td class="align_center">3514</td><td class="align_center">4607</td><td class="align_center">5594</td><td class="align_center">6546</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Relation between the neck radius and resonance frequency, (<svg height="11.927pt" id="M72" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 13.0619 11.927" width="13.0619pt" 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="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path d="M452 282C452 397 389 451 302 451C268 451 227 441 188 422C95 377 24 281 24 154C24 65 70 -12 173 -12C240 -12 297 16 342 52C418 113 452 201 452 282ZM359 282C359 163 308 66 247 39C237 35 225 32 212 32C151 32 114 79 114 157C114 301 180 380 223 398C240 405 250 408 265 408C315 408 359 369 359 282Z" id="g50-112"></path></g></svg> = 5.0 mm, <svg height="11.927pt" id="M73" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 11.2716 11.927" width="11.2716pt" 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="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 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" id="g50-106"></path></g></svg> = 4.5 mm).</div>

Advances in Condensed Matter Physics

tab1

Table 1

Table 1: The Effect of Geometrical Parameters on Resonance Characteristics of Acoustic Metamaterials with Negative Effective Modulus 