Forward Analysis of Love-Wave Scattering due to a Cavity-Like Defect

<table class="fixed-width table-group" id="tab2"><tr><td><table class="table"><colgroup><col style="width:6.36em"/><col style="width:4.59em"/><col style="width:10.08em"/><col style="width:11.38em"/></colgroup><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Frequency <svg height="9.42945pt" id="M166" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -9.22306 8.42472 9.42945" width="8.42472pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="8.32509" x="0" y="-8.52081"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z" id="g113-246"></path></g></svg></td><td class="align_center">Modal</td><td class="align_center">Reflection coefficients</td><td class="align_center">Transmission coefficients</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">0.8</td><td class="align_center">Modal 1</td><td class="align_center">0.00039 − 0.07060i</td><td class="align_center">−0.00582 + 0.03457i</td></tr><tr><td class="align_left" rowspan="2">5</td><td class="align_center">Modal 1</td><td class="align_center">−0.04383 + 0.10690i</td><td class="align_center">0.01638 + 0.02342i</td></tr><tr><td class="align_center">Modal 2</td><td class="align_center">−0.11344 + 0.06911i</td><td class="align_center">0.07724 + 0.11906i</td></tr><tr><td class="align_left" rowspan="3">9.5</td><td class="align_center">Modal 1</td><td class="align_center">−0.03315 + 0.08802i</td><td class="align_center">0.00531 + 0.00383i</td></tr><tr><td class="align_center">Modal 2</td><td class="align_center">−0.19330 + 0.36373i</td><td class="align_center">0.04204 + 0.03600i</td></tr><tr><td class="align_center">Modal 3</td><td class="align_center">−0.22045 − 0.05598i</td><td class="align_center">0.07071 + 0.09606i</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The transmission and reflection coefficients with truncated locations at <span class="nowrap"><svg height="12.4698pt" id="M163" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 72.2531 12.4698" width="72.2531pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="7.29424" x="0" y="-8.52081"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z" id="g113-121"></path></g><g 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viewbox="-0.0498162 -9.28833 13.5121 12.4698" width="13.5121pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z" id="g113-233"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M567 167L534 181C505 122 482 94 454 70C428 46 385 42 330 42C288 42 248 44 235 55C216 70 213 91 220 130L295 528C310 609 314 611 401 618L409 650H140L131 618C222 611 224 609 209 528L133 126C118 47 108 41 25 33L18 0H497C514 33 554 126 567 167Z" id="g50-77"></path></g></svg> being the Love wavelength for the lowest mode), for a circle arc defect at the bonding interface.</div>

Shock and Vibration

Forward Analysis of Love-Wave Scattering due to a Cavity-Like Defect

Table 2