Modeling and Dynamic Properties of a Four-Parameter Zener Model Vibration Isolator

<div>(a) Amplitude-frequency characteristic when <svg height="13.7134pt" id="M486" style="vertical-align:-5.36458pt" version="1.1" viewbox="-0.0498162 -8.34882 40.6099 13.7134" width="40.6099pt" 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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="789" vert-adv-y="789"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.192,3.132)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g190-102"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="425" vert-adv-y="425"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.105,3.132)"><path d="M515 -240V-213C445 -206 438 -202 438 -132V332C438 399 440 418 441 439L437 442C421 434 408 431 402 431C394 430 389 431 375 435C363 440 342 445 306 449C168 450 38 341 38 197C38 101 108 -12 253 -12L359 30V-130C359 -201 353 -207 274 -213V-240H515ZM359 60C340 51 316 44 285 44C211 44 128 109 128 230C128 348 194 408 262 408C294 408 336 392 359 366V60Z" id="g190-114"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="511" vert-adv-y="511"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.59,0)"><path d="M-161 592L-215 609L-427 -83L-372 -100L-161 592Z" id="g117-145"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="0" vert-adv-y="0"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,22.917,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,34.209,0)"><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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>. (b) Amplitude-frequency characteristic when <svg height="13.7134pt" id="M487" style="vertical-align:-5.36458pt" version="1.1" viewbox="-0.0498162 -8.34882 40.6099 13.7134" width="40.6099pt" 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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="789" vert-adv-y="789"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.192,3.132)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g190-102"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="425" vert-adv-y="425"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.105,3.132)"><path d="M515 -240V-213C445 -206 438 -202 438 -132V332C438 399 440 418 441 439L437 442C421 434 408 431 402 431C394 430 389 431 375 435C363 440 342 445 306 449C168 450 38 341 38 197C38 101 108 -12 253 -12L359 30V-130C359 -201 353 -207 274 -213V-240H515ZM359 60C340 51 316 44 285 44C211 44 128 109 128 230C128 348 194 408 262 408C294 408 336 392 359 366V60Z" id="g190-114"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="511" vert-adv-y="511"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,22.917,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,34.18,0)"><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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>.</div>

Shock and Vibration

fig14

Figure 14

Figure 14: Modeling and Dynamic Properties of a Four-Parameter Zener Model Vibration Isolator 