Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck considering Dry Friction

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/sv/volume-2015/839801/figures/839801.fig.006a.svgz" name="839801.fig.006a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Bifurcation diagram at <svg height="8.86839pt" id="M389" style="vertical-align:-3.05102pt" version="1.1" viewbox="-0.0498162 -5.81737 10.8789 8.86839" width="10.8789pt" 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="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path><glyph.data ascent="989" descent="-303" horiz-adv-x="447" vert-adv-y="447"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,5.811,3.001)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/sv/volume-2015/839801/figures/839801.fig.006b.svgz" name="839801.fig.006b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Bifurcation diagram at <svg height="8.86839pt" id="M390" style="vertical-align:-3.05102pt" version="1.1" viewbox="-0.0498162 -5.81737 10.8789 8.86839" width="10.8789pt" 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="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path><glyph.data ascent="989" descent="-303" horiz-adv-x="447" vert-adv-y="447"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,5.811,3.001)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></td></tr></table>

<div>Bifurcation diagram of <svg height="11.7574pt" id="M388" style="vertical-align:-3.16066pt" version="1.1" viewbox="-0.0498162 -8.59674 15.0675 11.7574" width="15.0675pt" 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="M782 650H541L536 618L564 614C597 609 604 600 584 574C535 508 486 451 437 395C394 473 361 533 343 575C331 605 335 610 375 615L400 618L407 650H156L147 618C222 612 230 608 267 537L375 330C277 214 186 117 163 96C108 43 97 38 27 32L18 0H265L274 32L251 35C204 41 202 47 224 80C264 138 327 213 397 293L504 80C520 48 516 42 472 36L440 32L433 0H707L716 32C627 38 622 43 581 121L455 361L629 548C685 606 696 610 775 618L782 650Z" id="g50-89"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="800" vert-adv-y="800"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.984,3.001)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> at two critical speeds.</div>

Shock and Vibration

fig6

Figure 6

Figure 6: Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck considering Dry Friction 