高等结构动力学大作业

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1、AdvancedStructuralDynamicsProjectThedynamicresponseandstabilityanalysisofthebeamunderverticalexcitationInstructor：Dr.LiWeiName：StudentID：1.Problemdescriptionandthepurposeoftheproject1.1calculationmodelAnEularbeamsubjectedtoanaxialforce.Pleasebuildthedifferentialequationofmotionanduseap

2、roperdifferencemethodtosolvethisdifferentialequation.Studythedynamicstabilityofthebeamrelatedtothefrequencyandamplitudeoftheforce.AsshownintheFig1.1.Figl.l1.2purposeandprocessarrangementa.learninghowtocreatemathematicalmodelofthecontinuoussystemandselectpropercalculationmethodtosolveit

3、.b.learninghowtobuildbeamvibrationequationandsolveMathieuequation.c.usingFloquettheorytojudgevibrationsystem’sstabilityandanalyzetherelationshipamongthefrequencyandamplitudeoftheforceanddynamicresponse.Thisprojectwillintroducetheestablishmentofthemathematicalmodelofthecontinuoussystemi

4、nsection2,themovementequationandthenumericalsolutionofusingMATLABinsection3，ApplyingFloquenttheorytostudythedynamicstabilityofthebeamrelatedtothefrequencyandamplitudeoftheforceinsection4.Inthelastoftheproject,wegetsomeconclusionsinsection5.1.themathematicalmodelofthesystemFig.2.1Thegeo

5、metricmodelofthebeamandforce-simplifieddiagramisshowninFig.2.1.Weassumethatitsstiffness(EI)isconstantandthedeflectionofthebeamissmall,andtheboundaryconditionsissimplysupport.Nowthebeamsubjectedtoanaxialforce.Weassumetheforceisequaltocoscot.WeselectthelengthofAxinanypositionofthebeam，th

6、efree-bodydiagramisshowninFig.2.2.Fig.2.2Usingequationsofmovementequilibrium,thatistosay:+TEFv=(Am)6/v(1)(2)Fromequation(1)，wewillget:S(x,r)-5(x+=pAx—-dt2Divideequation(3)byAxandtakethelimit:dSd2yThensynthesizeequation(2)，wecanget:A/(x+Ax,r)-A/(%，Z)+F[)’(x+Ax，z)-y(x,t)]-S(%+A.r,Z)Ar=0

7、Divideequation(5)byAxandtakethelimit:^f^=sdxdxCombineequation(4)with(6):d2Md2yd2y^+F^+PA^=°AndM(x，t)=£ICombineequation(7)with(8):WeknowElisaconstant,so£/lz+F(^+^=oInequation(10)，misthemassofunitlength.Nowwewilluseassumed-modesmethod.Named=U，)sinZ77ZXm^+E1芊T”，、芊Id—dtsin—=0n=l,2;(4)(5)