forced response in time domain：时域响应

《forced response in time domain：时域响应》由会员上传分享，免费在线阅读，更多相关内容在应用文档-天天文库。

1、ResponseoflinearSDOFtoarbitraryexcitationObjective:LearnhowtofindtheresponseofalinearSDOFsystemtoagiveninput(excitation)Preliminarydefinitions:Response=naturalresponse+forcedresponseNaturalresponse:solutionofequationofmotionofthesystemwhentheexcitationiszero.Theexpressionforn

2、aturalresponsecontainsconstants.17Forcedresponse:anysolutionofequationofmotionofthesystemfornonzeroexcitation.Ifthenaturalresponsetendstozerowhentimetendstoinfinityandthelimitoftheforcedresponseastimegoestoinfinityexistsandisbounded(notinfinite),thenthelimitiscalledsteadystat

3、eresponse.Transientresponse:Processofgoingfrominitialstatetosteadystate.17SteadystateTransientresponseTransientresponseisduetoboththeapplicationoftheforceandthenonzeroinitialconditions17Outlineofthischapter1.Impulseresponsefunction2.Responsetoarbitraryexcitation3.Shockspectru

4、m4.Numericalcalculationofresponse17ImpulseresponsefunctionImpulsefunction:idealizationofshort-durationforceappliedsuddenlyForcetimeForcetimeArea=Idealization17Impulseresponsemkch(t)δ(t)Findresponseofsingledegreeoffreedomsystemtoaunitimpulse:Case1:z<117Ifimpulsewasappliedattim

5、e,τ,thenImpulseresponsesoftwosystemswithnaturalfrequency6.28rad/secanddampingratios0.1and0.8.Slopeis1/mhere17Observations:·Transientresponsediesoutfasterwhendampingincreases.·Displacementovershootdecreaseswithdamping.·Maximumdisplacementdoesnotoccurexactlyattimeequaltoonefour

6、thofaperiod,unlessdampingiszero.·Slopejustafterimpulsehasbeenapplied(i.e.att=0+)is1/m.17Case2:Overdampedsystem,z>1Case3:Criticallydampedsystem,z=117ResponsetoarbitraryexcitationFirst,assumethatsystemisatrestatt=0.Idea:Usesuperpositionprinciple.Splitexcitationtosumofimpulses.F

7、indresponsetoeachimpulseandsumuptheresponses.Equivalentequationforresponse:Theabovearecalledconvolutionintegrals.17Ifsystemisnotatrestatt=0,thentheresponseisthefreevibrationresponseduethenonzeroinitialconditionsplustheaboveconvolutionintegral17StepresponseUnitstepfunction1tCo

8、nsiderunderdampedsystemsonly.Responsetounitstep:17Timetopeak,tp=half