Out-of-Plane Elastic Waves in 2D Models of Solids: A Case Study for a Nonlocal Discretization Scheme with Reduced Numerical Dispersion

<div>Wave propagation for the wavelength <svg height="9.49473pt" id="M121" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 35.9357 9.49473" width="35.9357pt" 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="M547 100L523 123C489 76 461 62 452 62C442 62 433 71 427 109C405 243 387 408 378 495C360 666 322 710 263 710C230 710 182 688 161 667L170 639C184 646 203 651 218 651C247 651 272 634 288 562C297 521 300 485 304 436C230 267 111 104 24 11L33 -12L116 6C163 73 263 255 311 362L347 84C355 26 373 -12 406 -12C440 -12 489 12 547 100Z" id="g50-233"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="571" vert-adv-y="571"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,11.096,0)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g><g 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274 403 303 403C330 403 360 395 374 387Z" id="g50-98"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="514" vert-adv-y="514"></glyph.data></g></svg> (b) registered for different interaction regions when <svg height="8.80314pt" id="M123" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -8.59674 32.8954 8.80314" width="32.8954pt" 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="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="888" vert-adv-y="888"></glyph.data></g><g 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Due to symmetry, only the displacements determined for of a half of the model are presented.</div>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: Out-of-Plane Elastic Waves in 2D Models of Solids: A Case Study for a Nonlocal Discretization Scheme with Reduced Numerical Dispersion 