Parallel Piezoelectric Shunt Damping of Rotationally Periodic Structures

<div>Natural frequencies (normalized to <svg height="9.16067pt" id="M22" style="vertical-align:-3.16062pt" version="1.1" viewbox="-0.0498162 -6.00005 13.1754 9.16067" width="13.1754pt" 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="M624 292C624 400 569 451 537 451C520 451 497 442 490 436L489 427C521 404 550 351 550 280C550 170 513 51 423 51C383 51 361 87 361 150C361 197 384 301 397 339L391 343L310 328C307 297 301 249 293 212C270 102 223 56 182 56C144 56 114 93 114 172C114 278 161 369 243 430L223 457C99 392 24 290 24 156C24 43 81 -12 141 -12C187 -12 247 32 286 88C295 31 325 -12 380 -12C431 -12 475 16 511 49C581 113 624 195 624 292Z" id="g50-246"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="648" vert-adv-y="648"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.099,3.001)"><path d="M453 623H65C60 580 56 530 46 472H80C103 538 110 548 175 548H389C310 380 195 168 90 0L98 -12L175 -2C273 206 366 408 462 610L453 623Z" id="g50-56"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>) versus nodal diameters <svg height="6.20645pt" id="M23" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -6.00005 6.78059 6.20645" width="6.78059pt" 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="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" id="g50-111"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="512" vert-adv-y="512"></glyph.data></g></svg> for the bladed drum of Figure <a href="../fig1/">1</a> (for a given rotation speed <svg height="8.85534pt" id="M24" style="vertical-align:-0.04981041pt" version="1.1" viewbox="-0.0498162 -8.80553 10.1211 8.85534" width="10.1211pt" 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="M727 145L694 147C669 79 660 74 614 74H536C582 128 696 227 696 364C696 547 564 666 388 666C215 666 78 544 78 361C78 224 189 126 240 74H155C117 74 102 83 79 147L48 145L64 0H313L320 21C290 72 182 208 182 360C182 527 261 628 387 628S593 523 593 362C593 199 488 69 456 21L461 0H709L727 145Z" id="g50-153"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="768" vert-adv-y="768"></glyph.data></g></svg>).</div>

Advances in Materials Science and Engineering

fig2

Figure 2

Figure 2: Parallel Piezoelectric Shunt Damping of Rotationally Periodic Structures 