Engineering Basic Mechanics Ⅱ Dynamics 工程基础力学 Ⅱ 动力学 课件 Chapter 10 Vibrations.pptx

Chapter10Vibrations

MainContents§10.1UndampedFreeVibration§10.2UndampedForcedVibration§10.3ViscousDampedFreeVibration§10.4ViscousDampedForcedVibration

Vibrationistheperiodicmotionofabodyorsystemofconnectedbodiesdisplacedfromapositionofequilibrium.Vibrationbelongstothesecondcategoryofkineticproblems－solvemotionproblemsthroughknownactiveforcesResearchmethodofvibrationproblems?Motionanalysis；?Forceanalysis；?Selecttheappropriatekinetictheorem；?Establishandsovledifferentialequationsofmotion.?Selecttheappropriategeneralizedcoordinates；Introduction

Differentialequationsoffreevibration10.1UndampedfreevibrationEstablishOxaxis,theequilibriumpositionofparticleMascoordinateoriginO,whenthepositionofMisx,elasticforceFactingontheMcanbedescribedasBecauseSo(naturalfrequency)Let

Wehavethisisahomogeneous,second-order,linear,differentialequationwithconstantcoefficients.Usingthemethodsofdifferentialequations,itsgeneralsolutionisdefiningnewconstantsCand?Camplitudeofvibration?phaseangleτperiodffrequecy10.1Undampedfreevibration

Example10-1mvldetermien（1）vibrationregulationofblock;（2）maxiumtensioninthewirerope.10.1UndampedfreevibrationAblockm＝6000kgissuspendfromwireropethatpassesoverawheel.Theelasticmodulusandcross-sectionalareaareE＝200GPaandA＝2.89×10－4m2,respectively.Theblockisbeingloweredwithcostantvelocityv＝0.25m/s,whentheblockisloweredtobel＝25m,thewireropesuddenlyjams,Solution:thesystemcanbeconsideredasspring-blocksystem,thestiffnessofspringisN/m

Wecanassumethatwhenthewireropeisjammed,thetimeist＝0,attheinstant,thepositionofblockisinitialequilibriumposition.Choosethedownwarddistancexofblockasgeneralizdcoordinate,