《振动力学基础》课件

振动力学基础Introduction toVibrationsHarmonicMotion1DefinitionHarmonic motion is atype ofperiodic motioncharacterized byasinusoidal waveform.2EquationThe equation of harmonicmotionisx=A sinωt+φ,where x isdisplacement,A is amplitude,ωis angularfrequency,t istime,andφis phaseangle.3ApplicationsHarmonic motionis foundin numerousfields such as mechanicalengineering,physics,and music.Single Degreeof FreedomSystemDefinition ExampleEquation ofMotionA single degree ofA simplependulum is an Theequationofmotionfreedom system is aexample ofa singlefor asingle degree ofsystem thathas onlyone degreeof freedomfreedom systemis mx+independent coordinatesystem.kx=Ft,where misthat determinesits mass,xisacceleration,motion.k isstiffness,x isdisplacement,and Ftisthe externalforcingfunction.Free UndampedVibrationDefinition ExplanationApplicationsFree undamped vibration Asimple mass-spring Freeundamped vibrationisoccurs when a systemis systemisanexample offree observedin musicalfree to oscillatewithout anyundampedvibration,where instrumentssuch astuningexternal forcesand thereis themass oscillatesback andforks andstringno dampingpresent.forth aroundits equilibriuminstruments.position.Free DampedVibration1DefinitionFree dampedvibration occurs whena systemisfreetooscillate,but thereisa dampingforce presentthat reducesthe amplitude of thevibration overtime.2Types of DampingCommon typesof dampinginclude viscousdamping,structural damping,and materialdamping.3Effect onVibrationDamping reducesthe amplitudeof thevibration andcauses thesystem toreacha steady-state condition.Forced Vibration1DefinitionForced vibrationoccurswhenasystemis subjectedto anexternalforce ormotion.2ResonanceResonance isa phenomenonthat canoccur inforced vibrationwhenthe frequencyof theexternal forcematches thenatural frequencyofthe system.3ApplicationsForced vibrationis encounteredin variousengineering applications,suchasearthquake engineeringand mechanicalsystems.Power Absorptionin SingleDegree ofFreedomSystemsRole ofDamping ApplicationsBenefitsDamping insingle degreeofDampingtechniques areEffective powerabsorptionfreedom systemshelps inused invarious systems such helpsin improvingthedissipating theenergy andas shockabsorbers andperformance,comfort,andreducing theamplitudeofspring mattressesto controlsafety ofsystemssuchasvibrations,resulting inand absorbvibrations.vehicle suspensions.efficient powerabsorption.Multiple Degreeof FreedomSystems1Definition2Complexity3StructuralAnalysisA multipledegreeofMultiple degreeoffreedom systemisafreedom systemsMultiple degreeofsystem withmore exhibitmore complexfreedom systemsarethan oneindependent behaviorcompared toextensively studiedincoordinate thatsingledegreeof thefield ofstructuraldetermine itsmotion.freedom systemsdue analysisto understandtothe interactionand thedynamic responsecouplingof multipleof complexstructures.degrees offreedom.。