Comparison Study on the Exact Dynamic Stiffness Method for Free Vibration of Thin and Moderately Thick Circular Cylindrical Shells

<div>Differences between the first frequencies under each <svg height="6.1673pt" id="M243" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.6501 6.1673" width="6.6501pt" 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="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g></svg> with different <svg height="11.439pt" id="M244" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 18.1982 11.439" width="18.1982pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.185,0)"><path d="M368 703H309L44 -163H104L368 703Z" id="g113-48"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="412" vert-adv-y="412"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.546,0)"><path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g></svg>.</div>

Shock and Vibration

fig9

Figure 9

Figure 9: Comparison Study on the Exact Dynamic Stiffness Method for Free Vibration of Thin and Moderately Thick Circular Cylindrical Shells 