Robust Optimum Design of Multiple Tuned Mass Dampers for Vibration Control in Buildings Subjected to Seismic Excitation

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Method</td><td class="align_center">Positions <svg height="14.8578pt" id="M51" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -14.808 10.678 14.8578" width="10.678pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-8.586)"><path d="M567 230V280H69V230H567Z"></path></g><g transform="matrix(.013,0,0,-0.013,-1.901,-8.586)"><path d="M901 255C861 290 790 361 716 442L694 427L796 280H69V230H796L694 83L716 68C790 149 861 220 901 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,1.264,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g></svg></td><td class="align_center"><span style="width: 85.8217ptpx;"><svg height="12.4894pt" id="M52" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -9.3079 85.8217 12.4894" width="85.8217pt" 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="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><g transform="matrix(.013,0,0,-0.013,8.008,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 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423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z"></path></g><g transform="matrix(.013,0,0,-0.013,58.329,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">Robust design</td><td class="align_center">[0000000111]</td><td class="align_center">1313.857; 915.187; 1468.914</td><td class="align_center">43.358; 200.407; 11.058</td><td class="align_center">0.01588</td></tr><tr><td class="align_left">Alternative 1</td><td class="align_center">[0010010010]</td><td class="align_center">1313.857; 915.187; 1468.914</td><td class="align_center">43.358; 200.407; 11.058</td><td class="align_center">0.01828</td></tr><tr><td class="align_left">Alternative 2</td><td class="align_center">[1111111111]</td><td class="align_center">369.796 for each one of the 10 TMDs</td><td class="align_center">25.482 for each one of the 10 TMDs</td><td class="align_center">0.02712</td></tr><tr><td class="align_left">Alternative 3</td><td class="align_center">[0000000001]</td><td class="align_center">3697.958</td><td class="align_center">254.823</td><td class="align_center">0.02121</td></tr><tr><td class="align_left">Alternative 4</td><td class="align_center">[0000000001]</td><td class="align_center">4296.981</td><td class="align_center">115.874</td><td class="align_center">0.01617</td></tr><tr><td class="align_left">Alternative 5</td><td class="align_center">[0000000111]</td><td class="align_center">1419.331; 1448.020; 1447.742</td><td class="align_center">39.478; 312.519; 9.683</td><td class="align_center">0.01603</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Comparison between robust design and alternative methods.</div>

Shock and Vibration

tab4

Table 4

Table 4: Robust Optimum Design of Multiple Tuned Mass Dampers for Vibration Control in Buildings Subjected to Seismic Excitation 