基于复合单元模型的轴向功能梯度梁的振动分析.pdf

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1、中国科技论文在线http://www.paper.edu.cnVibrationanalysisofaxiallyfunctionallygradedbeamswith#thecompositeelementmodel**5LIUJike,LVZhongrong(SchoolofEngineering,SunYat-senUniversity,Guangzhou510006,P.R.China)Abstract:Thispaperpresentsasimpleyetaccurateapproachtoanalyzethefreeandforcedvibrationsofaxiallyf

2、unctionallygraded(AFG)beams.ThegoverningequationsofthebeamisderivedbyLagrange’sequationsandthendiscretizedbythecompositeelementmethod.Numericalsimulations10arepresentedtoshowtheeffectsofYoung’smodulusvariation,massdensityvariation,andslendernessratios,onthedynamiccharacteristicsoftheAFGbeams.The

3、naturalfrequenciesobtainedfromtheproposedmethodarefoundtobeincloseagreementwiththosefromfiniteelementandothermethods.TheforcedvibrationresponsesoftheAFGbeamarealsocalculatedfromtheproposedmethodandcomparedwiththoseobtainedfromthefiniteelementmethod(FEM).Timehistoriesfrom15bothmethodsarefoundtoma

4、tchverywell.ThisfurtherindicatesthecorrectnessofthepresentmethodforforcedvibrationanalysisoftheAFGbeam.Keywords:solidmechanics;compositeelement;freeandforcedvibrations;response;axiallyfunctionallygradedbeam200IntroductionFunctionallygradedmaterials(FGMs)areinhomogeneouscompositeswithmaterialprop

5、ertiesvaryingcontinuouslythroughoutthegradientdirection,whichwasfirstdevelopedinJapanin1984bySendaiGroup.FGMshavegreatadvantagesoverthetraditionalhomogeneousmaterialsduetocontinuoustransitionofmaterialproperties.Withincreasingapplicationsof25FGMs,newmethodologiestopredicttheirmechanicalbehaviors

6、havebeenextensivelystudiedduringthepastfewdecades.EngineersandresearchershavebeeninterestedinFGMsformany[1-3]years,becausetheyhavepromisingmechanicalandthermalproperties.Atthepresenttime,FGbeamscanbedividedintotwocategoriesbasedontheorientateddirections.Oneisthematerialconstituentsvaryinginthick

7、nessdirection,whichhavebeen[4-6][7,8]30intensivelystudied.Theotherismaterialconstituentsvaryinginaxialdirection.Forthelatterone,theproblemofanalyzingbending,vibrationandstabilitybecomesmorecomplicatedduetothegoverningequatio