機械振動噪聲學FundamentalsofMechanicalVibrationandNoisePro.柳貢民

辦公地點:三甲動力裝置工程技術研究所Email:liugongmin@Tel:82569458,82569468科書（Textbook）:

趙玫等，機械振動與噪聲學，科學出版社，

2004參考書（ReferenceBooks）:

W.T.ThomsonandM.D.Dahleh,TheoryofVibrationswithApplications(5thed.),PrenticeHall,19972.?

R.F.Barron,IndustrialNoiseControlandAcoustics,MarcelDekker,2003?鄭兆昌主編，機械振動（上冊），機械工業出版社，1980?商大中，動力分析基礎，哈爾濱工程大學出版社，1999?季文美，機械振動，科學出版社，19851.1MechanicalVibrationandControl

Chapter1Introduction1.1.1SummaryofMechanicalVibrationVibratingPhenomenaintheWorldVibrationarefoundinmanybranchesofscienceandengineering1.1MechanicalVibrationandControl

Chapter1Introduction1.1.1SummaryofMechanicalVibrationUndesirablevibrations：

Vehicle;Noise;Machines&Structures;Earthquake;PowerunitsineverykindsofvesselsmaycausevibrationsUsefulvibrations：

Stringvibration;harmonicoscillator,resonator;Vibratingroadroller;Vibratingfeeder;Vibratingformingmachine.1.1MechanicalVibrationandControl

Chapter1Introduction1.1.1SummaryofMechanicalVibration1.1MechanicalVibrationandControl

Chapter1Introduction1.1.2BasicConceptMechanicalVibration?Researchaim?Vibrationisaphenomenathatabodyorstructureoscillatesaboutsomespecifiedreferencepoint.Vibrationiscommonlyexpressedintermsoffrequency,amplitudeandPhaseangle.1.Eliminationorsuppressionofundesirablevibrations2.Generationofthenecessaryformsandquantitiesofusefulvibrations1.1MechanicalVibrationandControl

Chapter1Introduction1.1.3ModelofVibrationSystem離散系統（集中參數系統）Discretesystem(Lumpedparametersystem)連續系統（分布參數系統）Continuoussystem(Distributedparametersystem)1.1MechanicalVibrationandControl

Chapter1Introduction1.1.4ClarificationofMechanicalVibrations(1)按自由度分(Accordingtothedegreeoffreedom)Theleastnumberofmutuallyindependentparameters(coordinates)requiredtouniquelydefineamaterialsystem'spositioninspace,time,etc單自由度系統振動(singledegreeoffreedom)

多自由度系統振動(multipledegreeoffreedom)連續系統振動(continuoussystem)Chapter1Introductionθθz單自由度系統振動(singledegreeoffreedom)

多自由度系統振動(multipledegreeoffreedom)ABABChapter1Introduction模型與自由度(Modelanddegreeoffreedom)1.1MechanicalVibrationandControl

Chapter1Introduction1.1.4ClarificationofMechanicalVibrations(2)按激勵形式分(Accordingtotheexcitation)：自由振動(freevibration)

(noforce)

強迫振動(forcedvibration)(externalforce)Freevibration

—theperiodicmotionoccurringwhenanelasticsystemisdisplacedfromitsequilibriumposition;

Forcedvibration

—thevibrationresultingfromtheapplicationofanexternalforce；

1.1MechanicalVibrationandControl

Chapter1Introduction1.1.4ClarificationofMechanicalVibrations(3)按系統的響應分(Accordingtothesystemresponse)：簡諧振動(harmonicvibration);周期振動(periodicvibration)瞬態振動(transientvibration);隨機振動(randomvibration)Harmonicvibration

—Oscillationsinwhichmotionisperiodicwithtimeintheformofasinecurve.Periodicvibration—Anoscillatorymotionwhoseamplitudepatternrepeatsafterfixedincrementsoftime.Transientvibration—Temporarilysustainedvibrationofamechanicalsystem.Itmayconsistofforcedvibration.

Randomvibration—Avibrationwhoseinstantaneousamplitudeisnotspecifiedatanyinstantoftime.1.1MechanicalVibrationandControl

Chapter1Introduction1.1.4ClarificationofMechanicalVibrations(4)按系統微分方程分(AccordingtotheDifferentialEquation

)：線性振動(linearvibration)

非線性振動(nonlinearvibration)LinearVibration

—Lineardifferentialequation;(superposition)Nonlinearvibration

—Nonlineardifferentialequation

Bifurcation&ChaosVibrationSystemExcitationResponse√?√VibrationanalysisorResponseanalysisVibrationSystemExcitationResponse√?√VibrationenvironmentpredictionVibrationSystemExcitationResponse√?√VibrationdesignorSystemidentification1.1MechanicalVibrationandControl

Chapter1Introduction1.1.5ProblemsofMechanicalVibrationandSolvingMethods1.1MechanicalVibrationandControl

Chapter1IntroductionTheoreticalanalysis1.1.5ProblemsofMechanicalVibrationandSolvingMethodsRealsystemMechanicsprincipleD.E.NumericalsolutionAnalyticalsolutionComputersimulationMathematicaltoolsVibrationcharacteristicsExperimentVibrationmonitoring,testing,andexperimentationareimportantaswellinthedesign,implementation,maintenance,andrepairofengineeringsystems.

Chapter1IntroductionAlltheseareimportanttopicsofstudyinthefieldofvibrationengineering,1.1.5ProblemsofMechanicalVibrationandSolvingMethods1.1MechanicalVibrationandControl

控制方法：新的保護罩用打孔金屬薄板和金屬絲網制成。消減激振源1.1MechanicalVibrationandControl

Chapter1Introduction1.1.6MechanicalVibrationControlMethods

壓榨機的飛輪和傳動帶的保護罩是主要的噪聲源。保護罩用實體金屬薄片制成。1.1MechanicalVibrationandControl

Chapter1Introduction1.1.6MechanicalVibrationControlMethods其它措施：避免共振；減振與隔振。1.2MechanicalNoiseandControl

Chapter1Introduction1.2.1SoundandNoiseSoundWaveisanydisturbancethatispropagatedinanelasticmediumSoundSourceisanobjectthatcausedvibrationofmediumparticlesSoundFieldisaspacewherethesoundwaveexists1.2MechanicalNoiseandControl

Chapter1Introduction1.2.1SoundandNoiseNoiseisanyunwantedsoundperceivedbythehearingsenseofahumanisamixtureofsoundwaveswithdifferentfrequenciesandstrengths1.2MechanicalNoiseandControl

Chapter1Introduction1.2.2NoiseEffectsHearingandHealthExcessivenoisecanimpairhearing,mayalsoputstressontheheart,thecirculatorysystem,andotherpartsofthebodyTechnicalStandardsForexample,thepass-bynoisenationalstandardsforcars,84dB(A)(1979),78dB(A)(1985),74dB(A)(2006).MilitaryVehiclesRequireHighstealthcapabilitiesQuietworkingandlivingenvironment1.2MechanicalNoiseandControl

Chapter1Introduction1.2.3ClarificationsofMechanicalNoise(1)按聲源形成機理分(Accordingtothemechanismsofsoundsourcegeneration)：結構振動輻射噪聲

(Radiatednoisefromstructurevibration)

流體動力性噪聲(Fluiddynamicnoise)(2)按聲波傳遞的媒質分(Accordingtothemediuminwhichthesoundwavetransmission)：空氣噪聲(Air-bornenoise)結構噪聲

(Structure-bornenoise)

1.2MechanicalNoiseandControl

Chapter1Introduction1.2.4MethodsofMechanicalNoiseControlEverysituationinnoisecontrolinvolvesasystemcomposedofthreebasicelements:Source,Path,andReceiverLowNoiseDesignistheidealmethodfortheMechanicalProductNoiseControlClass1Chapter2VibrationofSingle-Degree-of-FreedomSystem(SDOF)

2.1DifferentialEquationofVibration2.2FreeVibration2.3ForcedVibration2.4VibrationIsolationOutline:Mechanicalmodelofphysicalsystem2.1DifferentialEquationofVibrationAshaftingofdieselengine柴油機軸系扭振模型1.ermediateshaft6.screwpropellerMechanicalmodelofphysicalsystem2.1DifferentialEquationofVibrationDiscretizationofphysicalsystemMasselementSpringelementDampingelement2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibration

ElasticMountedDieselGeneratingSetExample2-Discretizationofphysicalsystem2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibrationExample2-1

ElasticmountedGeneratingSet

SDOFSystemDiscretizationofphysicalsystem2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibrationMasselement質量元件Inelastic,rigidbody，kineticenergystorageelements是無彈性的剛體,儲存動能的元件Translation平移：

Force力,mass質量

&acceleration加速度

Units量綱:N、kg、m/s

2。

Rotation旋轉：

Moment力矩,momentofinertia轉動慣量

&angularacceleration角加速度

Units量綱:Nm、kgm2、rad/s2

Discretizedmechanicalsystem2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibrationSpring(elastic)element彈性元件Potentialenergystorageelements是勢能儲存元件Force力,stiffness剛度

&displacement位移Units量綱:N,N/m&mMoment力矩,torsionstiffness扭轉剛度

&angle角位移Units量綱:Nm,Nm/rad&radTranslation平移：Rotation旋轉：Discretizedmechanicalsystem2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibrationDampingelement阻尼元件Energydissipationelements耗能元件Force力,dampingcoefficient阻尼系數&velocity速度Units量綱:N,Ns/m&m/s

。

Moment力矩,torsiondampingcoefficient扭轉阻尼系數&angularvelocity角速度

Units量綱:Nm,Nms/rad&rad/sTranslation平移：Rotation旋轉：Discretizedmechanicalsystem2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibration(1)Forcemethod2.1.2MethodstoEstablishDifferentialEquationSteps：1.Generalizedcoordinate建立廣義坐標2.

Drawadiagramofequilibriumofforcesofthemasselement作質量元件的隔離體受力分析圖

.Normalformofthevibrationequation建立振動微分方程并整理成標準的形式2.1DifferentialEquationofVibration(1)ForcemethodExample2-2SDOFdampingsystemGeneralizedcoordinate.建立廣義坐標

(direction方向,origin原點)Mechanicsprinciple

力學定律2.1DifferentialEquationofVibration2.1.2MethodstoEstablishDifferentialEquationEquilibriumofforcesatthemasselement質量受力的平衡singlependulumGeneralizedcoordinate

θ.(direction,origin)

EquilibriumofmomentsatthejointD’AlembertPrinciple(1)ForcemethodExample2-32.1DifferentialEquationofVibration2.1.2MethodstoEstablishDifferentialEquationMultipleMassSystemGeneralizedcoordinate

θx1=aθ,x2=2a

θ

(1)ForcemethodExample2-42.1DifferentialEquationofVibration2.1.2MethodstoEstablishDifferentialEquationNewton2ndlawform1andm2

(1)ForcemethodExample2-42.1DifferentialEquationofVibration2.1.2MethodstoEstablishDifferentialEquationMomentlawform3whereorLinearizationVibrationDifferentialEquation3.Usingprincipleofconservationofenergy(2)EnergymethodSteps：

1.Generalizedcoordinate.2.1DifferentialEquationofVibration2.1.2MethodstoEstablishDifferentialEquation2.KineticenergyV,potentialenergyU&dissipationenergyP(2)EnergymethodExample2-5

：

2.1DifferentialEquationofVibration2.1.2MethodstoEstablishDifferentialEquation1.Generalizedcoordinate..Kineticenergy動能T、potentialenergy勢能U3.UsingprincipleofconservationofenergyMultipleMassSystemGeneralizedcoordinate

θ

(direction,origin)

x1=aθ,x2=2a

θ

Example2-6(2)Energymethod2.1DifferentialEquationofVibration2.1.2MethodstoEstablishDifferentialEquationKineticenergyVPotentialenergyUDissipationenergyP

Usingprincipleofconservationofenergy

Example2-6(2)Energymethod2.1DifferentialEquationofVibration2.1.2MethodstoEstablishDifferentialEquationMulti-mass(orspring,damping)elementsGeneralformofvibrationequationforSDOFsystemTranslation：Rotation：equivalence2.1DifferentialEquationofVibration2.1.3EquivalentSystemSingle-mass(orspring,damping)elementParallelspringsEquivalentstiffnessParallelsprings2.1DifferentialEquationofVibration2.1.3EquivalentSystem(1)EquivalentstiffnessMethods：

1Definitionofstiffness。

2Potentialenergy

SeriesSpringsSeriesSpringsEquivalentstiffness2.1DifferentialEquationofVibration2.1.3EquivalentSystemParallelsystemSeriessystem(2)Equivalentdamping2.1DifferentialEquationofVibration2.1.3EquivalentSystemExample2-7EquivalentmasstoApointSpring-lever-masssystemKineticEnergy(originalsystem)KineticEnergy

(equivalentsystem)∵(3)Equivalentmass

(kineticenergyequivalence)2.1DifferentialEquationofVibration2.1.3EquivalentSystemProblems2-2,2-3,2-4,2-5,2-6,2-9,2-12HomeWorksPages41&42Thankyouandhaveaniceday!

對如右圖所示系統，可建立坐標系x，畫出質量m的受力隔離體圖，利用牛頓定律列出運動方程。Let

，wehave

Thesolutionoftheequationaboveis

2.2FreeVibration2.2.1UndampedSystemAssumingtheinitialconditiontobe

設初始條件為

Thesolutionequationundertheinitialconditionwillbe

則在此初始條件下的響應為2.2FreeVibration2.2.1UndampedSystemtOr或Here

式中Circularnaturalfrequency

圓頻率Amplitude振幅Phaseangle相角Period周期Naturalfrequency頻率2.2FreeVibration2.2.1UndampedSystemAsystem’speriodandfrequencyaredeterminedbyitsphysicalproperties.

Discussion討論Thedisplacement,velocityandaccelerationofthesystemareasfollowed系統的位移、速度、加速度分別為Theyareallharmonicfunction

可見系統的位移、速度、加速度都做簡諧變化，且速度、加速度分別比位移超前90度和180度角。這個相位差角是不變的。2.2FreeVibration2.2.1UndampedSystemFromtheequationsoftheamplitudeandphaseangleWeknowthattheyarealldeterminedbytheinitialconditions.Thisisthecharacteristicsofnaturalvibration.系統振動的振幅和相角都決定于初始條件，這正是振動系統自由振動的特性。Butasystem’speriodandfrequencyaredeterminedbyitsphysicalproperties.但系統的周期和頻率則取決于它的物理特性。2.2FreeVibration2.2.1UndampedSystemthestaticdisplacementTheenergymethodtheequationofmotionThenaturalfrequencyof