结构动力学课件-3responsetoarbitrary-step-and-pilseexcita

,CHAPTER5.RESPONSETOIMPULSIVELOADING,5.1GEGERALNATUREOFIMPUSIVELOADING,FIGURE5-1Arbitraryimpulsiveloading,Relativelyshortduration,Dampinghasmuchlessimportanceincontrollingthemaximumresponse,Onlytheundampedresponsetoimpulsiveloadswillbeconsidered,FIGURE5-2Half-sine-waveimpulse,FIGURE5-3Rectangularimpulse,FIGURE5-4Triangularimpulse,5.2SINEWAVEIMPULSE,CHAPTER5.RESPONSETOIMPULSIVELOADING,Forimpulsiveloadswhichcanbeexpressedbysimpleanalyticalfunctions,closedformsolutionsoftheequationsofmotioncanbeobtained.,thesinglehalfsinewaveimpulse,twophases:,forcedvibrationphase,freevibrationphase,PhaseI:,Assumingthesystemstartsfromrest,Sinceitisindeterminatefor,LHospitalsrulemustbeappliedtoobtainauseableexpressionforthisspecialcase.Takingthisaction,oneobtains,PhaseII:,Thefreevibrationmotionwhichoccursduringthisphase,dependsonthedisplacementandvelocityexistingattheendofPhaseI;Eq.(233)initsresponseratioformthisfreevibrationresponseisshowntobe,For,requiringonceagaintheuseofLHospitalsruleleadingto,CHAPTER5.RESPONSETOIMPULSIVELOADING,CHAPTER5.RESPONSETOIMPULSIVELOADING,themaximumvalueofresponsedependsontheratiooftheloaddurationtotheperiodofvibrationofthestructure,FIGURE5-5Responseratiosduetohalf-sinepulse,CHAPTER5.RESPONSETOIMPULSIVELOADING,5.3RECTANGULARIMPULSE,PhaseI.Thesuddenlyappliedloadwhichremainsconstantduringthisphaseiscalledasteploading.Theparticularsolutiontotheequationofmotionforthiscaseissimplythestaticdeflection,Usingthisresult,thegeneralresponseratiosolution,inwhichthecomplementaryfreevibrationsolutionconstantshavebeenevaluatedtosatisfytheatrestinitialconditions,iseasilyfoundtobe,CHAPTER5.RESPONSETOIMPULSIVELOADING,PhaseII.,Takingthevectorsumofthetwoorthogonalcomponentsinthisexpressiongives,showingthatthemaximumresponsetotherectangularimpulsevariesasasinefunctionfor,CHAPTER5.RESPONSETOIMPULSIVELOADING,5.4SHOCKORRESPONSESPECTRA,themaximumresponsedependsonlyontheratiooftheimpulsedurationtothenaturalperiodofthestructure.Itisusefultoplotthemaximumvalueofresponseratioasafunctionofforvariousformsofimpulsiveloading,commonlyknownasdisplacementresponsespectra.,FIGURE5-6Displacement-responsespectra(shockspectra)forthreetypesofimpulse,CHAPTER5.RESPONSETOIMPULSIVELOADING,5.5APPROXIMATEANALYSISOFIMPULSIVELOADRESPONSE,Aconvenientapproximateprocedureforevaluatingthemaximumresponsetoashortdurationimpulsiveload,whichrepresentsamathematicalexpressionofthissecondconclusion,maybederivedasfollows.Theimpulsemomentumrelationshipforthemassmmaybewritten,Theresponseafterterminationofloadingisthefreevibration,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,6.1ANALYSISTHROUGHTHETIMEDOMAIN,FormulationofResponseIntegral,UndampedSystem,FIGURE6-1DerivationoftheDuhamelintegral(undamped),CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,Duhamelintegralequation,unitimpulseresponsefunction,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,Under-CriticallyDampedSystem,NumericalEvaluationofResponseIntegral,UndampedSystem,Todeveloptheseprocedures,useismadeofthetrigonometricidentity,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,UnderCriticallyDampedSystem,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,FIGUREE6-2Responseofwatertowertoblastload,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,6.2ANALYSISTHROUGHTHEFREQUENCYDOMAIN,TheFouriertransformofConvolutionintegralform,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,DiscreteFourierTransform(DFT),Tobepractical,thetimehistoryofanactionoraresponsemustbepresentedindiscretetimeseries,sotheFourierTransformmustbecarriedoutfordiscretevalueseries,thatistheDFT.,mistheordernumberofsamplingvalue.,TriangularSeriesDenotethesamplingnumberisN,andtheequaltimeincrementis,thenthedurationofthediscretetimeseriesis,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,Totally2(N/2+1)coefficientstobedetermined.However,wehave,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,Substitutingkbyl,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,Multiplythetwosidesby,ToobtainthesumfrommtoN-1,wehave,Changetheorderofmandl,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,k=0,k=1toN/2-1,k=N/2,k=0toN/2,Inthesameway,wehave,k=1toN/2-1,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,FourierSpectrum,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,LowestFrequency:,HighestFrequency:,NyquistFrequency,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,ComplexFourierSeries,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,Dueto,Wehave,Thesumofthirdandforthtermsinxm,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,Thenwehave,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,define,Dueto,EulerFormula,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,FastFourierTransform(FFT),J.W.GooleyandJ.W.Tukey,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,原序列,第一次对分,第二次对分,第三次对分,CHAPTER6.RESPONSETOGENERALDYNAMICLOADING:SUPERPOSITIONMETHODS,第三次合成,第一次合成,第二次合成,最后一次对分,CHAPTER6.RESPONSETOG