阻抗与导纳.pdf

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1、高等结构动力学阻抗与导纳VibrationcontrolVibrationProblemModelling(MobilityandUnderstandproblemImpedanceMethods)SolveProblemMeasurementMobilityandImpedance•TheresponseofastructuretoaharmonicforcecanbeexpressedintermsofitsmobilityorimpedanceAtfrequencythevelocitycanFVbewrittenincomplex

2、notationv(t)=VejtGenerallinearVisthecomplexamplitude.systemSimilarlyfortheforcef(t)=FejtThemobilityisdefinedasTheimpedanceisdefinedasVjFjMobilityImpedanceFjVj•Iftheforceandvelocityareatthesamepointthisisa‘point’mobility•Iftheyareatdifferentpointsitisa‘trans

3、fer’mobilityNotethatbothmobilityandimpedancearefrequencydomainquantitiesFrequencyResponseFunctions(FRFs)AccelerationForceAccelerance=ApparentMass=ForceAccelerationVelocityForceMobility=Impedance=ForceVelocityDisplacementForceReceptance=DynamicStiffness=ForceDisplacementMob

4、ilityandImpedanceMethods•Thetotalresponseofasetofcoupledcomponentscanbeexpressedintermsofthemobilityoftheindividualcomponents•Inthesimplestcaseeachcomponenthastwoinputs(oneateachend)whichpermitcouplingFF12GenerallinearsystemVV12•Thetwoparametersateachinputpointareforce,F,a

5、ndvelocity,V.SimpleIdealisedElements•SpringFkfkf12xxx12SoFkXf1kx1x2VFKVBecauseXthenjjf2kx2x1Sotheimpedanceofaspringisffgivenby12•nomassZFkk•forcepassesthroughVjitunattenuatedjtjtNotethattheforceisinquadraturewiththeAssumeandfFexXevelocity.Thusaspringi

6、sareactiveAlso,blockoneendsothatx20elementthatdoesnotdissipateenergySimpleIdealisedElements•ViscousdampercFcff12Vv1v2SoFcVf1cv1v2Sotheimpedanceofadamperisf2cv2v1givenbyffF12ZccV•nomassorelasticity•forcepassesthroughitunattenuatedNotethattheforceisinphasewitht

7、hevelocity.ThusadamperisaresistivejtjtelementthatdissipatesenergyAssumeandfFevVeAlso,blockoneendsothatv20SimpleIdealisedElements•MassFf1f2mmXxSoFmXffmx12BecauseXjVthenFjmVfmxf21Sotheimpedanceofamassisgivenby•rigid•forcedoesnotpassFZjmthroughitunattenuatedm

8、VjtjtAssumeandfFexXeNotethattheforceisinquadraturewiththeAlso,setoneendtobefreeveloci