Model Reduction Technique Tailored to the Dynamic Analysis of a Beam Structure under a Moving Load

<div>Comparison of (a) wheel-rail contact force <svg height="12.4067pt" id="M240" style="vertical-align:-3.408751pt" version="1.1" viewbox="-0.0498162 -8.99795 22.7151 12.4067" width="22.7151pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,6.937,3.264)"><path d="M956 650H736V622C814 613 818 602 804 542C789 471 733 275 691 141H689C628 314 570 476 514 641H485C434 478 377 312 323 142H321C277 284 238 419 199 554C184 605 186 613 259 622V650H16V622C77 615 92 606 117 524C172 346 228 170 281 -11H312C363 151 419 312 475 488H477C528 343 597 150 652 -11H683C765 269 826 458 848 522C878 605 887 613 956 622V650Z" id="g190-88"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="971" vert-adv-y="971"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,16.145,3.264)"><path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z" id="g190-83"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="621" vert-adv-y="621"></glyph.data></g></svg> and (b) rail deflection at the contact point <svg height="13.1057pt" id="M241" style="vertical-align:-3.427799pt" version="1.1" viewbox="-0.0498162 -9.6779 11.9896 13.1057" width="11.9896pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,7.452,3.264)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z" id="g50-100"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="411" vert-adv-y="411"></glyph.data></g></svg> predicted by the proposed condensed models (DCM, IRS, and SEREP) for the analytical model.</div>

Shock and Vibration

fig8

Figure 8

Figure 8: Model Reduction Technique Tailored to the Dynamic Analysis of a Beam Structure under a Moving Load 