Time Period of the Vibration of the Circular Plate with Circular Variation Both in Thickness and Density

<div>Time period <svg height="8.68572pt" id="M144" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 9.95144 8.68572" width="9.95144pt" 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="M743 650H503L496 622L527 618C563 613 564 603 532 573C449 495 371 431 323 392C301 374 272 355 246 346L280 522C297 609 300 614 379 622L385 650H135L129 622C209 614 215 609 198 522L124 133C106 39 99 35 23 28L17 0H271L277 28C193 35 192 39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z"></path></g></svg> of the clamped circular plate vs. tapering parameter <span class="nowrap"><svg height="7.81145pt" id="M145" style="vertical-align:-0.2063899pt" version="1.1" viewbox="-0.0498162 -7.60506 8.77704 7.81145" width="8.77704pt" 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="M642 327C642 461 565 582 389 582C298 582 219 548 176 519L185 491C235 515 291 526 348 526C477 526 572 452 572 268C572 145 509 51 431 51C396 51 366 78 366 145C366 189 391 295 402 337L396 341L320 332C315 289 306 229 296 187C276 99 230 55 185 55C149 55 111 89 111 170C111 275 160 373 238 431L222 457C99 394 23 290 23 157C23 40 81 -12 142 -12C185 -12 254 33 293 86C301 31 340 -12 394 -12C437 -12 477 8 524 50C589 108 642 203 642 327Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

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Figure 2

Figure 2: Time Period of the Vibration of the Circular Plate with Circular Variation Both in Thickness and Density 