Flutter Boundary Prediction Based on Structural Frequency Response Functions Acquired from Ground Test

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static-preview.hindawi.com/articles/ijae/volume-2022/2058755/figures/2058755.fig.0013a.svgz" name="2058755.fig.0013a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b><span class="nowrap"><svg height="9.49473pt" id="M171" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 7.34169 9.49473" width="7.34169pt" 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="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z"></path></g></svg>-</span><svg height="8.8423pt" id="M172" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 9.35121 8.8423" width="9.35121pt" 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="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static-preview.hindawi.com/articles/ijae/volume-2022/2058755/figures/2058755.fig.0013b.svgz" name="2058755.fig.0013b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Nyquist curve at <svg height="11.8174pt" id="M173" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 13.5747 11.8174" width="13.5747pt" 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="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"><path d="M606 650H137L129 618C217 609 221 609 203 518L129 129C115 46 106 40 26 32L18 0H300L307 32C210 40 203 45 218 129L249 305H358C454 305 455 296 457 219H491L531 425H497C465 353 463 350 366 350H259L300 569C306 605 310 611 346 611H444C522 611 535 598 541 578C550 557 553 519 552 485L588 489L606 650Z"></path></g></svg></td></tr></table>

<div>GFBP curves of normal state at <span class="nowrap"><svg height="8.73137pt" id="M170" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.52498 47.6579 8.73137" width="47.6579pt" 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="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.361,0)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.765,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.028,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.268,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,41.232,0)"><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"></path></g></svg>.</span></div>

International Journal of Aerospace Engineering

fig13

Figure 13

Figure 13: Flutter Boundary Prediction Based on Structural Frequency Response Functions Acquired from Ground Test 