Plane Wave-Perturbative Method for Evaluating the Effective Speed of Sound in 1D Phononic Crystals

<div>Graphs of the effective mass density <svg height="14.3057pt" id="M149" style="vertical-align:-5.082641pt" version="1.1" viewbox="-0.0498162 -9.22306 29.0504 14.3057" width="29.0504pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="7.03326" x="0" y="-8.52081"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z" id="g113-239"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="539" vert-adv-y="539"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.033,3.864)"><path d="M384 109C349 76 310 59 268 59C197 59 123 113 120 245C240 248 367 259 384 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ascent="1007" descent="-369" horiz-adv-x="434" vert-adv-y="434"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.666,3.132)"><path d="M100 439H52L25 408L28 396H100V106C100 41 92 35 31 30V0H250V29C188 37 181 41 181 106V396H372V107C372 40 365 37 309 29V0H537V29C461 37 453 40 453 106V396H564C576 403 579 428 574 439H453V469C452 558 462 604 474 623S500 656 527 656C562 656 589 634 608 615C619 604 628 607 639 615C647 622 658 633 661 641C666 653 664 664 656 674C637 696 609 708 572 710C528 703 483 682 439 638C418 661 380 685 320 688C269 683 230 666 190 633C139 593 122 550 113 525S100 476 100 451V439ZM372 439H181V461C181 530 194 571 211 598C226 621 248 643 287 643C343 643 379 607 400 578C391 561 384 546 381 529C376 510 372 486 372 457V439Z" id="g58-26"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="572" vert-adv-y="572"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,18.712,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 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Advances in Materials Science and Engineering

fig7

Figure 7

Figure 7: Plane Wave-Perturbative Method for Evaluating the Effective Speed of Sound in 1D Phononic Crystals 