A Unified Approach of Free Vibration Analysis for Stiffened Cylindrical Shell with General Boundary Conditions

<table class="fixed-width table-group" id="tab5"><tr><td><table class="table"><colgroup><col style="width:1.78em"/><col style="width:4.27em"/><col style="width:4.24em"/><col style="width:4.27em"/></colgroup><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2"><span style="width: 6.6501ptpx;"><svg height="6.1673pt" id="M148" 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"></path></g></svg></span></td><td class="align_center" colspan="3"><svg height="8.68572pt" id="M149" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 12.9526 8.68572" width="12.9526pt" 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="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z"></path></g></svg>=15, <svg height="8.8423pt" id="M150" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 11.0475 8.8423" width="11.0475pt" 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="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z"></path></g></svg>=5, <svg height="9.49473pt" id="M151" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.66314 9.49473" width="6.66314pt" 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="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"></path></g></svg>=0</td></tr><tr class="thead"><td class="align_center">FEM</td><td class="align_center">GM</td><td class="align_center">present</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">0</td><td class="align_center">598.17</td><td class="align_center">595.34</td><td class="align_center">599.84</td></tr><tr><td class="align_left">1</td><td class="align_center">625.00</td><td class="align_center">623.45</td><td class="align_center">624.24</td></tr><tr><td class="align_left">2</td><td class="align_center">662.26</td><td class="align_center">661.42</td><td class="align_center">663.69</td></tr><tr><td class="align_left">3</td><td class="align_center">1098.20</td><td class="align_center">1096.37</td><td class="align_center">1099.48</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Comparison of natural frequencies of cylindrical shells with free boundaries.</div>

Mathematical Problems in Engineering

tab5

Table 5

Table 5: A Unified Approach of Free Vibration Analysis for Stiffened Cylindrical Shell with General Boundary Conditions 