振动理论与分析

ShanghaiUniversitySHUTheoryofVibrationwithApplicationDishanHuangDeptofMechEngandAuto2009SpringOfficehour:Monday~Friday9:00am~4:00pmOffice:304BearingBuildinginYanchangCampusTel:56331383(o)1振动理论与分析5/8/2024SHUOurheartbeatOurlungsoscillateWehearbecauseoureardrumvibratesVibrationevenmakesussnore2振动理论与分析5/8/2024SHU3振动理论与分析5/8/2024SHU4振动理论与分析5/8/2024SHU5振动理论与分析5/8/2024SHU6振动理论与分析5/8/2024SHU7振动理论与分析5/8/2024SHU8振动理论与分析5/8/2024SHU9振动理论与分析5/8/2024SHU10振动理论与分析5/8/2024SHU11振动理论与分析5/8/2024SHU12振动理论与分析5/8/2024SHUSimplestmodel13振动理论与分析5/8/2024SHUImprovedModel14振动理论与分析5/8/2024SHUImprovedModel15振动理论与分析5/8/2024SHUX1andx2replacedbyX6andθ

16振动理论与分析5/8/2024SHURobotModel17振动理论与分析5/8/2024SHU1.2HarmonicMotion18振动理论与分析5/8/2024SHUSimulationdatabyMatlab19振动理论与分析5/8/2024SHUFreeVibration ElementStiffnessElement：Spring20振动理论与分析5/8/2024SHUFreeVibration ElementStiffnessElement：BarinTension21振动理论与分析5/8/2024SHUFreeVibration ElementStiffnessElement：BeaminBending22振动理论与分析5/8/2024SHUFreeVibration ElementStiffnessElement：BeaminBending23振动理论与分析5/8/2024SHUFreeVibration ElementStiffnessElement：Torsion24振动理论与分析5/8/2024SHUFreeVibration ElementStiffnessCombination25振动理论与分析5/8/2024SHUFreeVibration ElementSpringinSeries26振动理论与分析5/8/2024SHUFreeVibration ElementSpringinParallel27振动理论与分析5/8/2024SHUFreeVibration ElementCase1ComplicateCaseIfk2=Keq=?28振动理论与分析5/8/2024SHUFreeVibrationEnergymethod129振动理论与分析5/8/2024SHUFreeVibrationEnergymethod130振动理论与分析5/8/2024SHUFreeVibration Energymethod131振动理论与分析5/8/2024SHUFreeVibrationEnergymethod132振动理论与分析5/8/2024SHUFreeVibrationEnergymethod133振动理论与分析5/8/2024SHUFreeVibrationEnergymethod134振动理论与分析5/8/2024SHUFreeVibrationEnergymethod135振动理论与分析5/8/2024SHUFreeVibrationEnergymethod136振动理论与分析5/8/2024SHUFreeVibration EnergyMethod2ThemaximumkineticThePotentialEnergyNaturalFrequencyWhydonotyouconsidermgθr1

37振动理论与分析5/8/2024SHUFreeVibration

RayleighMethodRayleighMethod---EffectiveMassProblem:SpringwithdistributedmassSolutionVelocityinthespring:LetthemassofspringmsThenkineticenergyPotentialenergy:Therefore38振动理论与分析5/8/2024SHULagrange’EquationForconservationsystemEnergyisDifferentialofTfunctionGeneralformofKineticenergy(1)(2)(3)(4)(5)From(3)and(4)obtain39振动理论与分析5/8/2024SHULagrange’EquationBytheuseofd(uv)=vdu+udv,get(6)(7)Substitutingequation(7)fromaboveequationBecauseof

Therefore40振动理论与分析5/8/2024SHULagrange’EquationLagrange’equationLetL=T-U41振动理论与分析5/8/2024`SHULagrange’EquationStep1kineticandpotentialenergyStep2letLagrangefunctionL=T-U=-{}42振动理论与分析5/8/2024SHULagrange’EquationL=T-U=-{}Step3MotionequationFori=1obtainBasedonAsthesamereason,obtain43振动理论与分析5/8/2024SHULagrange’EquationDependonkineticenergyDependonpotentialenergy44振动理论与分析5/8/2024SHULagrange’Equationθ1θ2energy45振动理论与分析5/8/2024SHULagrange’EquationMotionequationlinearization46振动理论与分析5/8/2024SHULagrange’Equation47振动理论与分析5/8/2024SHULagrange’Equation0MotionequationMatrixform48振动理论与分析5/8/2024SHULagrange’EquationGeneralforce49振动理论与分析5/8/2024SHULagrange’Equa