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1、,Fundamentals of Mechanical Vibration and Noise,Pro.柳贡民 办公地点:三甲 动力装置工程技术研究所Email:liugongmin,教科书（Textbook）:赵玫等，机械振动与噪声学，科学出版社，2004,参考书（Reference Books）:W.T.Thomson and M.D.Dahleh,Theory of Vibrations with Applications(5th ed.),Prentice Hall,1997,2.R.F.Barron,Industrial Noise Control and Acoustics,Mar
2、cel Dekker,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，1985,1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.1 Summary of Mechanical Vibration,Vibrating Phenomena in the World,Vibration are found in many branches of science and engineering,1.1 Mechanical
3、Vibration and Control,Chapter 1 Introduction,1.1.1 Summary of Mechanical Vibration,Undesirable vibrations：Vehicle;Noise;Machines,Power units in every kinds of vessels may cause vibrations,Useful vibrations：String vibration;harmonic oscillator,resonator;Vibrating road roller;Vibrating feeder;Vibratin
4、g forming machine.,1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.1 Summary of Mechanical Vibration,1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.2 Basic Concept,Mechanical Vibration?,Research aim?,Vibration is a phenomena that a body or structure oscillates about
5、some specified reference point.Vibration is commonly expressed in terms of frequency,amplitude and Phase angle.,1.Elimination or suppression of undesirable vibrations 2.Generation of the necessary forms and quantities of useful vibrations,1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1
6、.1.3 Model of Vibration System,连续系统（分布参数系统）Continuous system(Distributed parameter system),1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.4 Clarification of Mechanical Vibrations,(1)按自由度分(According to the degree of freedom),The least number of mutually independent parameters(coordin
7、ates)required to uniquely define a material systems position in space,time,etc,单自由度系统振动(single degree of freedom)多自由度系统振动(multiple degree of freedom)连续系统振动(continuous system),Chapter 1 Introduction,单自由度系统振动(single degree of freedom),多自由度系统振动(multiple degree of freedom),Chapter 1 Introduction,模型与自由度(
8、Model and degree of freedom),1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.4 Clarification of Mechanical Vibrations,(2)按激励形式分(According to the excitation)：自由振动(free vibration)(no force)强迫振动(forced vibration)(external force),Free vibration the periodic motion occurring when an elast
9、ic system is displaced from its equilibrium position;Forced vibration the vibration resulting from the application of an external force；,1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.4 Clarification of Mechanical Vibrations,(3)按系统的响应分(According to the system response)：简谐振动(harmonic
10、 vibration);周期振动(periodic vibration)瞬态振动(transient vibration);随机振动(random vibration),Harmonic vibration Oscillations in which motion is periodic with time in the form of a sine curve.Periodic vibration An oscillatory motion whose amplitude pattern repeats after fixed increments of time.Transient vib
11、ration Temporarily sustained vibration of a mechanical system.It may consist of forced vibration.Random vibration A vibration whose instantaneous amplitude is not specified at any instant of time.,1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.4 Clarification of Mechanical Vibration
12、s,(4)按系统微分方程分(According to the Differential Equation)：线性振动(linear vibration)非线性振动(nonlinear vibration),Linear Vibration Linear differential equation;(superposition)Nonlinear vibration Nonlinear differential equation Bifurcation&Chaos,Vibration System,Excitation,Response,?,Vibration analysis or Respo
13、nse analysis,Vibration System,Excitation,Response,?,Vibration environment prediction,Vibration System,Excitation,Response,?,Vibration design or System identification,1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.5 Problems of Mechanical Vibration and Solving Methods,1.1 Mechanical
14、Vibration and Control,Chapter 1 Introduction,Theoretical analysis,1.1.5 Problems of Mechanical Vibration and Solving Methods,Experiment,Vibration monitoring,testing,and experimentation are important as well in the design,implementation,maintenance,and repair of engineering systems.,Chapter 1 Introdu
15、ction,All these are important topics of study in the field of vibration engineering,1.1.5 Problems of Mechanical Vibration and Solving Methods,1.1 Mechanical Vibration and Control,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,1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.6 Mechanical Vibration C
16、ontrol Methods,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。,1.1 Mechanical Vibration and Control,Chapter 1 Introduction,1.1.6 Mechanical Vibration Control Methods,其它措施：避免共振；减振与隔振。,1.2 Mechanical Noise and Control,Chapter 1 Introduction,1.2.1 Sound and Noise,Sound Waveis any disturbance that is propagated in
17、an elastic medium,Sound Sourceis an object that caused vibration of medium particles,Sound Fieldis a space where the sound wave exists,1.2 Mechanical Noise and Control,Chapter 1 Introduction,1.2.1 Sound and Noise,Noiseis any unwanted sound perceived by the hearing sense of a humanis a mixture of sou
18、nd waves with different frequencies and strengths,1.2 Mechanical Noise and Control,Chapter 1 Introduction,1.2.2 Noise Effects,Hearing and HealthExcessive noise can impair hearing,may also put stress on the heart,the circulatory system,and other parts of the body,Technical StandardsFor example,the pa
19、ss-by noise national standards for cars,84 dB(A)(1979),78 dB(A)(1985),74 dB(A)(2006).,Military Vehicles RequireHigh stealth capabilitiesQuiet working and living environment,1.2 Mechanical Noise and Control,Chapter 1 Introduction,1.2.3 Clarifications of Mechanical Noise,(1)按声源形成机理分(According to the m
20、echanisms of sound source generation)：结构振动辐射噪声(Radiated noise from structure vibration)流体动力性噪声(Fluid dynamic noise),(2)按声波传递的媒质分(According to the medium in which the sound wave transmission)：空气噪声(Air-borne noise)结构噪声(Structure-borne noise),1.2 Mechanical Noise and Control,Chapter 1 Introduction,1.2.
21、4 Methods of Mechanical Noise Control,Every situation in noise control involves a system composed of three basic elements:,Source,Path,and Receiver,Low Noise Design is the ideal method for the Mechanical Product Noise Control,Class 1,Chapter 2 Vibration of Single-Degree-of-Freedom System(SDOF),2.1 D
22、ifferential Equation of Vibration,2.2 Free Vibration,2.3 Forced Vibration,2.4 Vibration Isolation,Outline:,Mechanical model of physical system,2.1 Differential Equation of Vibration,A shafting of diesel engine 柴油机轴系扭振模型1.piston 2.connecting rod 3.crankshaft 4.flywheel 5.intermediate shaft 6.screw pr
23、opeller,Mechanical model of physical system,2.1 Differential Equation of Vibration,2.1.1.1 Discretization of physical system,Mass element,Spring element,Damping element,2.1.1 Mechanical Model of Physical System,2.1 Differential Equation of Vibration,Elastic Mounted Diesel Generating Set,Example 2-1,
24、2.1.1.1 Discretization of physical system,2.1.1 Mechanical Model of Physical System,2.1 Differential Equation of Vibration,Example 2-1,Elastic mounted Generating Set,SDOF System,2.1.1.1 Discretization of physical system,2.1.1 Mechanical Model of Physical System,2.1 Differential Equation of Vibration
25、,Mass element质量元件Inelastic,rigid body，kinetic energy storage elements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,moment of inertia转动惯量&angular acceleration角加速度 Units量纲:Nm、kg m 2、rad/s 2,2.1.1.2 Discretized mechanical system,2.1.1 Mechanical M
26、odel of Physical System,2.1 Differential Equation of Vibration,Spring(elastic)element弹性元件Potential energy storage elements是势能储存元件,Force力,stiffness刚度&displacement位移Units量纲:N,N/m&m,Moment力矩,torsion stiffness扭转刚度&angle角位移Units量纲:Nm,Nm/rad&rad,Translation平移：,Rotation旋转：,2.1.1.2 Discretized mechanical sy
27、stem,2.1.1 Mechanical Model of Physical System,2.1 Differential Equation of Vibration,Damping element阻尼元件Energy dissipation elements耗能元件,Force力,damping coefficient阻尼系数&velocity速度Units量纲:N,Ns/m&m/s。,Moment力矩,torsion damping coefficient扭转阻尼系数&angular velocity角速度 Units量纲:Nm,Nms/rad&rad/s,Translation平移：
28、,Rotation旋转：,2.1.1.2 Discretized mechanical system,2.1.1 Mechanical Model of Physical System,2.1 Differential Equation of Vibration,(1)Force method,2.1.2 Methods to Establish Differential Equation,Steps：1.Generalized coordinate 建立广义坐标2.Draw a diagram of equilibrium of forces of the mass element作质量元件
29、的隔离体受力分析图.Normal form of the vibration equation 建立振动微分方程并整理成标准的形式,2.1 Differential Equation of Vibration,(1)Force method Example 2-2,SDOF damping system,Generalized coordinate.建立广义坐标(direction方向,origin原点),Mechanics principle 力学定律,2.1 Differential Equation of Vibration,2.1.2 Methods to Establish Diff
30、erential Equation,Equilibrium of forces at the mass element质量受力的平衡,single pendulum,Generalized coordinate.(direction,origin),Equilibrium of moments at the joint,DAlembert Principle,(1)Force method Example 2-3,2.1 Differential Equation of Vibration,2.1.2 Methods to Establish Differential Equation,Mul
31、tiple Mass System,Generalized coordinate x1=a,x2=2a,(1)Force method Example 2-4,2.1 Differential Equation of Vibration,2.1.2 Methods to Establish Differential Equation,Newton 2nd law for m1 and m2,(1)Force method Example 2-4,2.1 Differential Equation of Vibration,2.1.2 Methods to Establish Different
32、ial Equation,Moment law for m3,where,or,Linearization Vibration Differential Equation,3.Using principle of conservation of energy,(2)Energy method Steps：1.Generalized coordinate.,2.1 Differential Equation of Vibration,2.1.2 Methods to Establish Differential Equation,2.Kinetic energy V,potential ener
33、gy U&dissipation energy P,(2)Energy method Example 2-5：,2.1 Differential Equation of Vibration,2.1.2 Methods to Establish Differential Equation,1.Generalized coordinate.Kinetic energy 动能T、potential energy 势能U,3.Using principle of conservation of energy,Multiple Mass System,Generalized coordinate(dir
34、ection,origin)x1=a,x2=2a,Example 2-6,(2)Energy method,2.1 Differential Equation of Vibration,2.1.2 Methods to Establish Differential Equation,Kinetic energy V Potential energy U Dissipation energy P,Using principle of conservation of energy,Example 2-6,(2)Energy method,2.1 Differential Equation of V
35、ibration,2.1.2 Methods to Establish Differential Equation,Multi-mass(or spring,damping)elements,General form of vibration equation for SDOF system,Translation：,Rotation：,equivalence,2.1 Differential Equation of Vibration,2.1.3 Equivalent System,Single-mass(or spring,damping)element,Parallel springs,
36、Equivalent stiffness,Parallel springs,2.1 Differential Equation of Vibration,2.1.3 Equivalent System,(1)Equivalent stiffness Methods：1 Definition of stiffness。2 Potential energy,Series Springs,Series Springs,Equivalent stiffness,2.1 Differential Equation of Vibration,2.1.3 Equivalent System,Parallel
37、 system,Series system,(2)Equivalent damping,2.1 Differential Equation of Vibration,2.1.3 Equivalent System,Example 2-7 Equivalent mass to A point,Spring-lever-mass system,Kinetic Energy(original system),Kinetic Energy(equivalent system),(3)Equivalent mass(kinetic energy equivalence),2.1 Differential
38、 Equation of Vibration,2.1.3 Equivalent System,Problems 2-2,2-3,2-4,2-5,2-6,2-9,2-12,Home Works,Pages 41&42,Thank you and have a nice day!,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，we have,The solution of the equation above is,2.2 Free Vibration,2.2.1 Undamped System,Assuming the initial condi
39、tion to be 设初始条件为,The solution equation under the initial condition will be 则在此初始条件下的响应为,2.2 Free Vibration,2.2.1 Undamped System,Or 或,Here 式中,Circular natural frequency 圆频率Amplitude 振幅Phase angle 相角Period 周期Natural frequency 频率,2.2 Free Vibration,2.2.1 Undamped System,A systems period and frequency
40、 are determined by its physical properties.,Discussion 讨论,The displacement,velocity and acceleration of the system are as followed 系统的位移、速度、加速度分别为,They are all harmonic function 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。,2.2 Free Vibration,2.2.1 Undamped System,From the equations of th
41、e amplitude and phase angle,We know that they are all determined by the initial conditions.This is the characteristics of natural vibration.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。,But a systems period and frequency are determined by its physical properties.但系统的周期和频率则取决于它的物理特性。,2.2 Free Vibration,2.2.1 Un
42、damped System,the static displacement,The energy method,the equation of motion,The natural frequency of the undamped system can be determined by,Vibration characteristics,2.2 Free Vibration,2.2.1 Undamped System,Initial displacement 10-3m Initial velocity 10-2m/s,Example 2-8,What is the free vibrati
43、on responses of the following systems?,2.2 Free Vibration,2.2.1 Undamped System,Example 2-8,2.2 Free Vibration,2.2.1 Undamped System,Example 2.3-2,2.2 Free Vibration,2.2.1 Undamped System,Example 2.3-2,2.2 Free Vibration,2.2.1 Undamped System,Example 2-9求如右图所示物体沿光滑斜面振动的方程及响应。已知斜面倾角=30,m=1千克，k=4900N/
44、m。在开始运动时弹簧无伸长，速度为零。,Solution:Lets erect the coordinate as shown in the figure,and take the equilibrium position as the origin point 建立坐标如图所示，以系统静平衡位置为坐标原点。,We may easily get the motion equation of the system 可列出系统的运动微分方程为,As derived above,the solution of the equation is 按照前面的推导，它的解为,2.2 Free Vibrati
45、on,2.2.1 Undamped System,The initial condition of this question is that the velocity is zero and the displacement equals to the static distortion 对本题，系统的初始速度为零，初始位移为弹簧静变形的负值。即,而固有圆频率为,所以，将初始条件代入解的表达式，得到,2.2 Free Vibration,2.2.1 Undamped System,Torsional vibration,2.2 Free Vibration,2.2.1 Undamped System,扭振系统,当量系统,轴：只有弹性，没有惯性kt：Torsional stiffness（Unit:kg m 2）,圆盘：只有惯性，没有弹性J：Moment of inertia（Unit:Nm/rad）,Generalized coordinate,Moment law,Problems-1,3-5,Home Works,Pages 83&84,Thank you and have a nice day!,
