关于铰支微梁横向受迫振动的高阶应变研究(英文)

关于铰支微梁横向受迫振动的高阶应变研究(英文)Introduction:In recent years, with the development of civil engineering and m

() 关于铰支微梁横向受迫振动的高阶应变研究英文 Introduction: Inrecentyears,withthedevelopmentofcivilengineeringand mechanicalengineering,thestudyofmicro-beamstructureshas becomeincreasinglyimportant.Thebehaviorofmicro-beamsis differentfromthatofordinarybeamsbecausethesizeof micro-beamsissmaller.Thisdifferencemakesthecalculationof strainanddeflectioncomplex.Thestudyofhigh-orderstrain analysisofmicro-beamsisvitalinunderstandingthestructural behaviorofthemicro-beam.Inthispaper,weaimtostudythe high-orderstrainanalysisofhinged-supportedmicro-beamunder transverseloading. 1.TheoreticalBackground: Thebehaviorofmicro-beamshasbeenstudiedusing Bernoulli-Eulerbeamtheory.Inthistheory,thebeamisassumed tobeastraightprismaticbeamwithconstantcross-section.The beamisassumedtobeloadedtransversely,anditsdeflectionand strainarecalculatedusingdifferentialequations.However,the Bernoulli-Eulerbeamtheoryhaslimitedapplicabilitywhenthesize ofthebeambecomesverysmall.Thereasonbehindthisisthat thebeam'saspectratiochangeswiththesizeofthebeam,andas theaspectratiodecreases,thebeam'sin-planedeformation becomesmoreprominent.Therefore,higher-orderstrainanalysis isrequiredtoaccuratelydeterminethestrainanddeflectionof micro-beams. 2.High-orderStrainAnalysisofHinged-supported Micro-Beam: Consideramicro-beamoflengthL,heighth,andthicknesst. Thebeamissupportedbyahingeatoneendandisloadedwitha transverseforcep(t)attheotherend.Letthedeflectionofthe beambedenotedbyw(x,t),wherexrepresentsthelongitudinal axisofthebeam.UsingBernoulli-Eulerbeamtheory,the governingequationforthedeflectionw(x,t)ofthebeamisgiven by: EI∂^4w(x,t)/∂x^4+µ∂^2w(x,t)/∂t^2=p(t)δ(x), whereErepresentstheYoung'smodulus,Irepresentsthe areamomentofinertia,andµrepresentsthemassdensityper