Vibration Control by Means of Piezoelectric Actuators Shunted with <i>LR</i> Impedances: Performance and Robustness Analysis

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left">Parameter</td><td align="center">Low value</td><td align="center">Medium value</td><td align="center">High value</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left"><svg height="15.5741pt" id="M505" style="vertical-align:-3.8522pt" version="1.1" viewbox="-0.0498162 -11.7219 20.548 15.5741" width="20.548pt" 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="M659 416L649 451C600 438 564 414 546 396C527 377 518 354 506 308C495 265 474 200 456 152C437 102 400 45 326 34L424 510L415 514L351 494L266 44C213 55 182 94 182 174C182 200 187 243 191 277C194 304 196 331 196 357C196 415 178 451 138 451C108 451 66 431 24 386L32 355C49 370 66 377 81 377C91 377 110 370 110 328C110 300 107 269 104 240C101 214 99 188 99 162C99 37 166 -5 257 -13L220 -202C215 -228 229 -251 236 -257L274 -218L318 -11C349 -4 378 8 400 21C444 48 489 89 518 157L586 327C601 369 619 393 659 416Z" id="g50-245"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="671" vert-adv-y="671"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.725,-5.872)"><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><g transform="matrix(.0091,0,0,-0.0091,8.138,3.693)"><path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z" id="g50-108"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="509" vert-adv-y="509"></glyph.data></g><rect height="0.69159" width="6.74619" x="13.6716" y="-8.7166"></rect><g transform="matrix(.013,0,0,-0.013,13.672,0)"><path d="M493 373C493 420 472 451 445 451C421 451 400 435 400 410C400 404 402 400 406 394S417 371 417 350C417 259 317 128 256 55H254C260 126 256 262 238 340C219 424 194 451 163 451C128 451 78 413 24 329L52 302C89 353 106 370 121 370C129 370 137 363 147 336C186 231 196 73 184 -16C152 -88 120 -192 112 -238L130 -257C157 -253 213 -227 231 -213C231 -187 234 -77 240 -23C251 -6 277 30 309 69C424 208 493 299 493 373Z" id="g50-225"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="517" vert-adv-y="517"></glyph.data></g></svg>  [rad<sup>2</sup>/s<sup>2</sup>]</td><td align="center">10</td><td align="center">1010</td><td align="center">1960</td></tr><tr><td align="left"><svg height="9.16067pt" id="M506" style="vertical-align:-3.16062pt" version="1.1" viewbox="-0.0498162 -6.00005 13.3764 9.16067" width="13.3764pt" 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="M624 292C624 400 569 451 537 451C520 451 497 442 490 436L489 427C521 404 550 351 550 280C550 170 513 51 423 51C383 51 361 87 361 150C361 197 384 301 397 339L391 343L310 328C307 297 301 249 293 212C270 102 223 56 182 56C144 56 114 93 114 172C114 278 161 369 243 430L223 457C99 392 24 290 24 156C24 43 81 -12 141 -12C187 -12 247 32 286 88C295 31 325 -12 380 -12C431 -12 475 16 511 49C581 113 624 195 624 292Z" id="g50-246"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="648" vert-adv-y="648"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.099,3.001)"><path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z" id="g50-108"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="509" vert-adv-y="509"></glyph.data></g></svg>  [rad/s]</td><td align="center"><span style="width: 42.334ptpx;"><svg height="8.54217pt" id="M507" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -8.33578 42.334 8.54217" width="42.334pt" 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 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26 5L34 -12C53 -12 94 -4 118 12C166 92 211 256 236 371L394 369C375 301 352 212 334 121C329 96 326 75 326 58C326 5 349 -12 381 -12C431 -12 482 25 519 66L504 97C480 80 448 64 432 64C419 64 410 80 422 154C432 217 450 303 466 365C499 365 536 366 546 369C557 384 570 409 583 449Z" id="g50-238"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="601" vert-adv-y="601"></glyph.data></g></svg></span></td><td align="center"><span style="width: 42.334ptpx;"><svg height="8.54217pt" id="M508" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -8.33578 42.334 8.54217" width="42.334pt" 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="M158 548H390L417 615L410 623H122L83 318C105 326 143 337 185 337C296 337 350 275 350 188C350 116 308 42 225 42C164 42 122 74 100 93C90 101 82 99 72 92C60 82 51 68 50 59C48 46 52 38 66 24C82 9 125 -12 172 -12C225 -11 292 15 346 59C408 108 437 166 437 226C437 309 371 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colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Selected values for <svg height="15.5741pt" id="M503" style="vertical-align:-3.8522pt" version="1.1" viewbox="-0.0498162 -11.7219 39.1225 15.5741" width="39.1225pt" 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="M659 416L649 451C600 438 564 414 546 396C527 377 518 354 506 308C495 265 474 200 456 152C437 102 400 45 326 34L424 510L415 514L351 494L266 44C213 55 182 94 182 174C182 200 187 243 191 277C194 304 196 331 196 357C196 415 178 451 138 451C108 451 66 431 24 386L32 355C49 370 66 377 81 377C91 377 110 370 110 328C110 300 107 269 104 240C101 214 99 188 99 162C99 37 166 -5 257 -13L220 -202C215 -228 229 -251 236 -257L274 -218L318 -11C349 -4 378 8 400 21C444 48 489 89 518 157L586 327C601 369 619 393 659 416Z" id="g50-245"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="671" vert-adv-y="671"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.725,-5.872)"><path d="M414 144C384 79 371 75 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Shock and Vibration

tab4

Table 4

Table 4: Vibration Control by Means of Piezoelectric Actuators Shunted with <i>LR</i> Impedances: Performance and Robustness Analysis 

Shock and Vibration

Vibration Control by Means of Piezoelectric Actuators Shunted with LR Impedances: Performance and Robustness Analysis

Table 4