Analysis of Vibration Reduction by Damping Using Simple Analytical Modelling

<div>Kinetic energy level change of receiver beam by a passive damper. Excitation: top: <svg height="15.184pt" id="M94" style="vertical-align:-3.6024pt" version="1.1" viewbox="-0.0498162 -11.5816 32.9346 15.184" width="32.9346pt" 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="M774 30C773 39 771 49 769 58C758 52 747 48 732 48C616 48 566 133 514 239C556 327 604 374 702 374C716 374 729 369 737 365C743 361 747 361 752 365C761 373 770 389 770 406C770 426 754 448 726 448C689 448 629 431 577 391C534 358 509 327 489 288C438 384 373 448 262 448C175 448 53 373 53 208C53 98 131 -12 262 -12C377 -12 426 52 472 147C516 51 579 -12 687 -12C713 -12 748 -2 774 30ZM451 198C415 110 363 21 272 21C195 21 145 114 145 240C145 353 194 415 250 415C357 415 409 304 451 198Z" id="g113-29"></path></g><g transform="matrix(.013,0,0,-0.013,14.383,-.336)"><path d="M778 808H735L485 -141H483L284 324L133 247L149 215L244 263L484 -298H486L778 808Z" id="g119-121"></path></g><rect height="0.65243" width="8.37729" x="24.4174" y="-10.8794"></rect><g transform="matrix(.013,0,0,-0.013,24.417,0)"><path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path></g></svg> RMS spectrum; bottom left: flat spectrum; bottom right: <svg height="12.7178pt" id="M95" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 22.9001 12.7178" width="22.9001pt" 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="M774 30C773 39 771 49 769 58C758 52 747 48 732 48C616 48 566 133 514 239C556 327 604 374 702 374C716 374 729 369 737 365C743 361 747 361 752 365C761 373 770 389 770 406C770 426 754 448 726 448C689 448 629 431 577 391C534 358 509 327 489 288C438 384 373 448 262 448C175 448 53 373 53 208C53 98 131 -12 262 -12C377 -12 426 52 472 147C516 51 579 -12 687 -12C713 -12 748 -2 774 30ZM451 198C415 110 363 21 272 21C195 21 145 114 145 240C145 353 194 415 250 415C357 415 409 304 451 198Z" id="g113-29"></path></g><g transform="matrix(.013,0,0,-0.013,14.383,0)"><path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path></g></svg> spectrum. Dotted line: damper rate giving best energy reduction.</div>

Shock and Vibration

fig10

Figure 10

Figure 10: Analysis of Vibration Reduction by Damping Using Simple Analytical Modelling 