Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

<div>Variation of the fundamental frequency (<span class="nowrap"><svg height="8.68572pt" id="M169" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 9.97754 8.68572" width="9.97754pt" 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="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z"></path></g></svg>)</span> with Young’s modulus (<i>E</i><sub>1</sub>/<i>E</i><sub>2</sub>), different boundary conditions, and different materials for the square plate (<span class="nowrap"><svg height="15.0796pt" id="M170" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -11.8981 54.2876 15.0796" width="54.2876pt" 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590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.281,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.544,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,39.784,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g></svg>).</span> (a) Sensor is PZT-4 and actuator is Ba<sub>2</sub>NaNb<sub>5</sub>O<sub>15</sub>; (b) sensor is BaTiO<sub>3</sub> and actuator is PZT-5A.</div>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques 

Figure 2 | Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques 