A Structural Pounding Formulation Using Systematic Modal Truncation

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/sv/volume-2018/6378085/figures/6378085.fig.006a.svgz" name="6378085.fig.006a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Displacement</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/sv/volume-2018/6378085/figures/6378085.fig.006b.svgz" name="6378085.fig.006b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Velocity</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/sv/volume-2018/6378085/figures/6378085.fig.006c.svgz" name="6378085.fig.006c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Acceleration</td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/sv/volume-2018/6378085/figures/6378085.fig.006d.svgz" name="6378085.fig.006d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Contact force</td></tr></table>

<div>Results for the displacement, the velocity, and the acceleration as well as the contact force with <span class="nowrap"><svg height="8.55521pt" id="M139" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 31.5818 8.55521" width="31.5818pt" 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="M766 88L752 113C719 83 690 64 681 64C674 64 672 74 679 103L724 292C758 436 724 448 701 448C680 448 666 442 639 429C594 407 514 350 441 252H439L447 289C476 423 450 448 419 448C398 448 379 441 355 427C307 400 234 344 162 249H160L180 324C203 409 197 448 170 448C144 448 82 413 23 349L35 321C57 343 96 374 108 374C115 374 117 371 111 341C87 227 57 112 24 -6L32 -12C53 -4 81 4 108 6C119 68 134 128 149 171C177 229 309 383 364 383C387 383 388 355 373 282C354 190 330 92 303 -6L309 -12C332 -4 356 3 386 6C396 63 411 122 424 171C458 236 590 383 642 383C658 383 664 369 652 315L603 91C587 20 593 -12 619 -12C642 -12 708 23 766 88Z" id="g113-110"></path></g><g transform="matrix(.013,0,0,-0.013,13.889,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,25.152,0)"><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></g></svg>.</span></div>

Shock and Vibration

A Structural Pounding Formulation Using Systematic Modal Truncation

Figure 6