Influence of Heterogeneous Contact Stiffness and Heterogeneous Friction Coefficient on Frictional Squeal

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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="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z" id="g113-247"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.005,3.132)"><path d="M546 97L529 123C499 91 459 65 450 65C443 65 439 73 445 106C468 226 496 341 523 451H513L436 424C423 357 412 311 403 276C356 195 245 59 190 59C165 59 158 99 166 135L236 445L227 451L152 428L60 18C43 -58 24 -145 24 -183C24 -237 43 -257 66 -257C96 -257 123 -236 130 -224L129 -216C115 -205 96 -156 96 -102C96 -57 105 -7 113 26H115C127 -1 137 -12 158 -12S198 -5 230 19C284 60 332 117 385 186H387C381 154 378 142 370 107C347 1 367 -12 388 -12C422 -12 492 32 546 97Z" id="g50-234"></path></g><g transform="matrix(.013,0,0,-0.013,14.287,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,25.55,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path></g><g transform="matrix(.013,0,0,-0.013,31.79,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path></g><g transform="matrix(.013,0,0,-0.013,34.754,0)"><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></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left" rowspan="3">The 1st unstable mode</td><td class="align_center">Dispersion</td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008a.svgz" name="6379201.tab-inline.008a" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008b.svgz" name="6379201.tab-inline.008b" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008c.svgz" name="6379201.tab-inline.008c" type="image/svg+xml"></object></td></tr><tr><td class="align_center">PD of frequency</td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008d.svgz" name="6379201.tab-inline.008d" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008e.svgz" name="6379201.tab-inline.008e" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008f.svgz" name="6379201.tab-inline.008f" type="image/svg+xml"></object></td></tr><tr><td class="align_center">PD of real part</td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008g.svgz" name="6379201.tab-inline.008g" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008h.svgz" name="6379201.tab-inline.008h" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008i.svgz" name="6379201.tab-inline.008i" type="image/svg+xml"></object></td></tr><tr><td class="align_left" colspan="5"><hr/></td></tr><tr><td class="align_left" rowspan="3">The 2nd unstable mode</td><td class="align_center">Dispersion</td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008j.svgz" name="6379201.tab-inline.008j" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008k.svgz" name="6379201.tab-inline.008k" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008l.svgz" name="6379201.tab-inline.008l" type="image/svg+xml"></object></td></tr><tr><td class="align_center">PD of frequency</td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008m.svgz" name="6379201.tab-inline.008m" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008n.svgz" name="6379201.tab-inline.008n" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008o.svgz" name="6379201.tab-inline.008o" type="image/svg+xml"></object></td></tr><tr><td class="align_center">PD of real part</td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008p.svgz" name="6379201.tab-inline.008p" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008q.svgz" name="6379201.tab-inline.008q" type="image/svg+xml"></object></td><td class="align_center"><object data="https://static.hindawi.com/articles/sv/volume-2018/6379201/figures/6379201.tab-inline.008r.svgz" name="6379201.tab-inline.008r" type="image/svg+xml"></object></td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Dispersions and probability densities of frequencies and real parts of the complex eigenvalues in the unstable region in Case 2.</div>

Shock and Vibration

tab8

Table 8

Table 8: Influence of Heterogeneous Contact Stiffness and Heterogeneous Friction Coefficient on Frictional Squeal 