A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/sv/volume-2018/8562079/figures/8562079.fig.0012a.svgz" name="8562079.fig.0012a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>The frequency of 4 clamped points’ plate with different thickness ratios <svg height="11.439pt" id="M254" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 18.3287 11.439" width="18.3287pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 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" id="g113-105"></path></g><g transform="matrix(.013,0,0,-0.013,6.708,0)"><path d="M368 703H309L44 -163H104L368 703Z" id="g113-48"></path></g><g transform="matrix(.013,0,0,-0.013,12.069,0)"><path d="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" id="g113-99"></path></g></svg> and theories</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/sv/volume-2018/8562079/figures/8562079.fig.0012b.svgz" name="8562079.fig.0012b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>The frequency of 16 clamped points’ plate with different thickness ratios <svg height="11.439pt" id="M255" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 18.3287 11.439" width="18.3287pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 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" id="g113-105"></path></g><g transform="matrix(.013,0,0,-0.013,6.708,0)"><path d="M368 703H309L44 -163H104L368 703Z" id="g113-48"></path></g><g transform="matrix(.013,0,0,-0.013,12.069,0)"><path d="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" id="g113-99"></path></g></svg> and theories</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/sv/volume-2018/8562079/figures/8562079.fig.0012c.svgz" name="8562079.fig.0012c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Error (%) of 4 clamped points’ plate with different thickness ratios<i> h</i>/<i>b</i> and theories</td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/sv/volume-2018/8562079/figures/8562079.fig.0012d.svgz" name="8562079.fig.0012d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Error (%) of 16 clamped points’ plate with different thickness ratios<i> h</i>/<i>b</i> and theories</td></tr></table>

<div>The frequency and error (%) of multipoint-supported plates with different thickness ratios<i> h/b</i> and theories.</div>

Shock and Vibration

fig12

Figure 12

Figure 12: A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges 