Parallel Piezoelectric Shunt Damping of Rotationally Periodic Structures

<div>Resonance condition to a rotating force. Zig-zag lines superimposed on the natural frequencies versus nodal diameters plot of the bladed drum with <svg height="8.80314pt" id="M37" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -8.59674 39.2501 8.80314" width="39.2501pt" 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="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="888" vert-adv-y="888"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.754,0)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.373,0)"><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><g transform="matrix(.013,0,0,-0.013,32.706,0)"><path d="M141 347C171 480 264 541 327 570C364 587 403 599 436 605L429 641C389 634 339 622 300 609C191 570 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 380 397 272 397C252 397 230 390 208 380L141 347ZM231 338C323 338 366 257 366 174C366 108 340 27 263 27C180 27 129 123 129 244C129 268 130 292 135 310C158 323 193 338 231 338Z" id="g50-55"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> blades. The resonance conditions are indicated by <svg height="7.56353pt" id="M38" style="vertical-align:-0.3629899pt" version="1.1" viewbox="-0.0498162 -7.20054 8.07242 7.56353" width="8.07242pt" 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="M547 55L345 261L547 468L508 508L306 301L104 508L65 468L267 261L65 55L104 14L306 221L508 14L547 55Z" id="g54-42"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g></svg>.</div>

Advances in Materials Science and Engineering

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Figure 3

Figure 3: Parallel Piezoelectric Shunt Damping of Rotationally Periodic Structures 