Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" colspan="5">Angular displacement</td></tr><tr class="thead"><td class="align_left">Scenarios</td><td class="align_center">Radius</td><td class="align_center">Case I</td><td class="align_center">Case II</td><td class="align_center">Case III</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center">15</td><td class="align_center"><span style="width: 48.0493ptpx;"><svg height="11.439pt" id="M35" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 48.0493 11.439" width="48.0493pt" 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="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.017,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.28,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.52,0)"><path d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 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<div>Different cases of equation (<a href="https://static.hindawi.com/articles/amse/volume-2022/1898124/figures/#EEq3" target="_blank">3</a>) based on variations in radius and angular displacement of a circular sector with <svg height="11.439pt" id="M33" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 43.5475 11.439" width="43.5475pt" 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="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.767,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.03,0)"><path d="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 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Advances in Materials Science and Engineering

tab1

Table 1

Table 1: Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning 