Modeling and Dynamic Analysis for a Motion of Mounted-Based Axisymmetric Rigid Body under Self-Excited Vibrations in an Attractive Newtonian Field

<div>The amplitude versus <i>F</i> at <span class="nowrap"><svg height="11.6399pt" id="M366" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -8.34882 34.46 11.6399" width="34.46pt" 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="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.969,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.776,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.038,0)"><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></svg>,</span> <span class="nowrap"><svg height="8.68572pt" id="M367" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 31.1643 8.68572" width="31.1643pt" 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><g transform="matrix(.013,0,0,-0.013,13.473,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.736,0)"><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></svg>,</span> and <span class="nowrap"><svg height="12.7178pt" id="M368" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 71.5021 12.7178" width="71.5021pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.806,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.068,0)"><path d="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.917,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.18,0)"><path d="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z"></path></g><g transform="matrix(.013,0,0,-0.013,53.713,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,64.976,0)"><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></svg>.</span> (a) <i>ε</i> = 0. (b) <i>ε</i> = 0.1. (c) <i>ε</i> = 0.25.</div>

Mathematical Problems in Engineering

fig9

Figure 9

Figure 9: Modeling and Dynamic Analysis for a Motion of Mounted-Based Axisymmetric Rigid Body under Self-Excited Vibrations in an Attractive Newtonian Field 

Figure 9 | Modeling and Dynamic Analysis for a Motion of Mounted-Based Axisymmetric Rigid Body under Self-Excited Vibrations in an Attractive Newtonian Field 