Frequencies of beams carrying multiple masses.pdf

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1、ARTICLEINPRESSJOURNALOFSOUNDANDVIBRATIONJournalofSoundandVibration268(2003)843–853www.elsevier.com/locate/jsviLettertotheEditorFrequenciesofbeamscarryingmultiplemasses:RayleighestimationversuseigenanalysissolutionsK.H.Low*SchoolofMechanicalandProductionEnginee

2、ring,NanyangTechnologicalUniversity,NanyangAvenue,Singapore639798,SingaporeReceived12November2002;accepted10March20031.IntroductionTherehavebeenextensiveresearchworksonthevibrationanalysisofbeamsorrodscarryingconcentratedmassesatarbitrarylocations.Approximatea

3、ndexactanalyseswereusedtoobtainthenaturalfrequencies[1–20].Theeigenfunctionofthebeam–masssystemswasobtainedbysatisfyingthedifferentialequationsofmotionandbyimposingthecorrespondingboundaryandcompatibilityconditionsassociatedtothemasses[13–15].Themethodoffreque

4、ncydeterminantwasthenusedtogeneratethefrequencyequation.Itwas,however,claimedthat,withthismethod,thenumberofthebeamequationsincreasesasthenumberofattachedmassesincreases.Therefore,themethodofLaplacetransformwassuggestedbyintroducingtheDiracdeltafunction(d)fort

5、heconcentratedmass[1–3,5,6,12].Inotherworks,GurgozeandBatan[11]concernedthenumericalsolutionofthetranscendentalfrequencyequation.ThecharacteristicequationwasobtainedbyusingRayleigh–Ritzmethod[17]andfreevibrationswereanalyzedbyusingtheLaplacetransformmethod[18]

6、.MauriziandBelles[19]comparedtwofundamentaltheoriesofbeamvibrations.OzkayaandPakdemirli[20]obtainedthefrequenciesfortheclamped–clampedbeamwithmassandsearchedapproximatesolutionsoffreeandforcednon-linearvibrationsusingaperturbationmethod.Lowetal.[21]foundthatth

7、eresultsofexperimentsandthetheorydidnotmatchwellforbeamsoflargeslendernessratioforcentre-loadedbeams.Differentassumedshapefunctionstoobtainthekineticandpotentialenergiesofthethreeclassicalbeamscarryingaconcentratedmasswerepresented[22,23].Alaterwork[24]showedt

8、hatthecorrelationbetweentheoryandexperimentswasmuchimprovedwhenstretchingeffectswereincluded.InRef.[25],thefundamentaleigenvalueofbeamscarryingconcentratedmasseswaspredictedmerelyf