机械振动噪声学一

机械振动噪声学FundamentalsofMechanicalVibrationandNoisePro.柳贡民

办公地点:三甲动力装置工程技术研究所Email:liugongmin@Tel:82569458,82569468科书（Textbook）:

赵玫等，机械振动与噪声学，科学出版社，

2004参考书（ReferenceBooks）:

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

R.F.Barron,IndustrialNoiseControlandAcoustics,MarcelDekker,2003•郑兆昌主编，机械振动（上册），机械工业出版社，1980•商大中，动力分析基础，哈尔滨工程大学出版社，1999•季文美，机械振动，科学出版社，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离散系统（集中参数系统）Discretesystem(Lumpedparametersystem)连续系统（分布参数系统）Continuoussystem(Distributedparametersystem)1.1MechanicalVibrationandControl

Chapter1Introduction1.1.4ClarificationofMechanicalVibrations(1)按自由度分(Accordingtothedegreeoffreedom)Theleastnumberofmutuallyindependentparameters(coordinates)requiredtouniquelydefineamaterialsystem'spositioninspace,time,etc单自由度系统振动(singledegreeoffreedom)

多自由度系统振动(multipledegreeoffreedom)连续系统振动(continuoussystem)Chapter1Introductionθθz单自由度系统振动(singledegreeoffreedom)

多自由度系统振动(multipledegreeoffreedom)ABABChapter1Introduction模型与自由度(Modelanddegreeoffreedom)1.1MechanicalVibrationandControl

Chapter1Introduction1.1.4ClarificationofMechanicalVibrations(2)按激励形式分(Accordingtotheexcitation)：自由振动(freevibration)

(noforce)

强迫振动(forcedvibration)(externalforce)Freevibration

—theperiodicmotionoccurringwhenanelasticsystemisdisplacedfromitsequilibriumposition;

Forcedvibration

—thevibrationresultingfromtheapplicationofanexternalforce；

1.1MechanicalVibrationandControl

Chapter1Introduction1.1.4ClarificationofMechanicalVibrations(3)按系统的响应分(Accordingtothesystemresponse)：简谐振动(harmonicvibration);周期振动(periodicvibration)瞬态振动(transientvibration);随机振动(randomvibration)Harmonicvibration

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

Randomvibration—Avibrationwhoseinstantaneousamplitudeisnotspecifiedatanyinstantoftime.1.1MechanicalVibrationandControl

Chapter1Introduction1.1.4ClarificationofMechanicalVibrations(4)按系统微分方程分(AccordingtotheDifferentialEquation

)：线性振动(linearvibration)

非线性振动(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：新的保护罩用打孔金属薄板和金属丝网制成。消减激振源1.1MechanicalVibrationandControl

Chapter1Introduction1.1.6MechanicalVibrationControlMethods

压榨机的飞轮和传动带的保护罩是主要的噪声源。保护罩用实体金属薄片制成。1.1MechanicalVibrationandControl

Chapter1Introduction1.1.6MechanicalVibrationControlMethods其它措施：避免共振；减振与隔振。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)按声源形成机理分(Accordingtothemechanismsofsoundsourcegeneration)：结构振动辐射噪声

(Radiatednoisefromstructurevibration)

流体动力性噪声(Fluiddynamicnoise)(2)按声波传递的媒质分(Accordingtothemediuminwhichthesoundwavetransmission)：空气噪声(Air-bornenoise)结构噪声

(Structure-bornenoise)

1.2MechanicalNoiseandControl

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

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

ElasticMountedDieselGeneratingSetExample2-Discretizationofphysicalsystem2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibrationExample2-1

ElasticmountedGeneratingSet

SDOFSystemDiscretizationofphysicalsystem2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibrationMasselement质量元件Inelastic,rigidbody，kineticenergystorageelements是无弹性的刚体,储存动能的元件Translation平移：

Force力,mass质量

&acceleration加速度

Units量纲:N、kg、m/s

2。

Rotation旋转：

Moment力矩,momentofinertia转动惯量

&angularacceleration角加速度

Units量纲:Nm、kgm2、rad/s2

Discretizedmechanicalsystem2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibrationSpring(elastic)element弹性元件Potentialenergystorageelements是势能储存元件Force力,stiffness刚度

&displacement位移Units量纲:N,N/m&mMoment力矩,torsionstiffness扭转刚度

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

。

Moment力矩,torsiondampingcoefficient扭转阻尼系数&angularvelocity角速度

Units量纲:Nm,Nms/rad&rad/sTranslation平移：Rotation旋转：Discretizedmechanicalsystem2.1.1MechanicalModelofPhysicalSystem2.1DifferentialEquationofVibration(1)Forcemethod2.1.2MethodstoEstablishDifferentialEquationSteps：1.Generalizedcoordinate建立广义坐标2.

Drawadiagramofequilibriumofforcesofthemasselement作质量元件的隔离体受力分析图

.Normalformofthevibrationequation建立振动微分方程并整理成标准的形式2.1DifferentialEquationofVibration(1)ForcemethodExample2-2SDOFdampingsystemGeneralizedcoordinate.建立广义坐标

(direction方向,origin原点)Mechanicsprinciple

力学定律2.1DifferentialEquationofVibration2.1.2MethodstoEstablishDifferentialEquationEquilibriumofforcesatthemasselement质量受力的平衡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动能T、potentialenergy势能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!

对如右图所示系统，可建立坐标系x，画出质量m的受力隔离体图，利用牛顿定律列出运动方程。Let

，wehave

Thesolutionoftheequationaboveis

2.2FreeVibration2.2.1UndampedSystemAssumingtheinitialconditiontobe

设初始条件为

Thesolutionequationundertheinitialconditionwillbe

则在此初始条件下的响应为2.2FreeVibration2.2.1UndampedSystemtOr或Here

式中Circularnaturalfrequency

圆频率Amplitude振幅Phaseangle相角Period周期Naturalfrequency频率2.2FreeVibration2.2.1UndampedSystemAsystem’speriodandfrequencyaredeterminedbyitsphysicalproperties.

Discussion讨论Thedisplacement,velocityandaccelerationofthesystemareasfollowed系统的位移、速度、加速度分别为Theyareallharmonicfunction

可见系统的位移、速度、加速度都做简谐变化，且速度、加速度分别比位移超前90度和180度角。这个相位差角是不变的。2.2FreeVibration2.2.1UndampedSystemFromtheequationsoftheamplitudeandphaseangleWeknowthattheyarealldeterminedbytheinitialconditions.Thisisthecharacteristicsofnaturalvibration.系统振动的振幅和相角都决定于初始条件，这正是振动系统自由振动的特性。Butasystem’speriodandfrequencyaredeterminedbyitsphysicalproperties.但系统的周期和频率则取决于它的物理特性。2.2FreeVibration2.2.1UndampedSystemthestaticdisplacementTheenergymethodtheequationofmotionThenaturalfrequencyof