Influence of Piezoelectric Performance on Nonlinear Dynamic Characteristics of MFC Shells

<div>Bifurcation diagram of the composite shell with the electric field increase. (a) <span class="nowrap"><svg height="11.8174pt" id="M157" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 33.7837 11.8174" width="33.7837pt" 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="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,15.054,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.59,0)"><path d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path></g></svg>.</span> (b) <span class="nowrap"><svg height="11.927pt" id="M158" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 33.7837 11.927" width="33.7837pt" 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="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.054,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.59,0)"><path d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path></g></svg>.</span></div>

Complexity

fig16

Figure 16

Figure 16: Influence of Piezoelectric Performance on Nonlinear Dynamic Characteristics of MFC Shells 