Numerical Investigation of Pull-In Instability in a Micro-Switch MEMS Device through the Pseudo-Spectral Method

<div>Line load density <svg height="9.39034pt" id="M105" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 10.794 9.39034" width="10.794pt" 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="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z" id="g113-114"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="491" vert-adv-y="491"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.318,3.132)"><path d="M398 365C398 411 356 451 297 451C250 451 198 430 151 397C65 336 24 230 24 139C24 14 97 -12 148 -12C198 -12 284 7 373 104L355 130C306 84 246 53 198 53C132 53 111 109 111 163V189C209 211 398 261 398 365ZM317 351C317 308 273 262 117 225C134 338 189 383 221 399C230 404 249 407 263 407C295 407 317 389 317 351Z" id="g50-102"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g></svg> on the cantilever beam near pull-in according to the pseudo-spectral approximation (<svg height="8.68572pt" id="M106" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 36.723 8.68572" width="36.723pt" 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" id="g113-66"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="703" vert-adv-y="703"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.767,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,24.03,0)"><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" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,30.27,0)"><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" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>).</div>

Modelling and Simulation in Engineering

fig9

Figure 9

Figure 9: Numerical Investigation of Pull-In Instability in a Micro-Switch MEMS Device through the Pseudo-Spectral Method 