机械振动噪声与控制PPT学习教案

1、会计学1 机械振动噪声与控制机械振动噪声与控制 2. R.F. Barron, Industrial Noise Control and Acoustics, Marcel Dekker, 2003 3. 郑兆昌主编， 机械振动（上册），机械工业出版社， 1980 4. 商大中，动力分析基础，哈尔滨工程大学出版社， 1999 5. 季文美，机械振动，科学出版社， 1985 第1页/共64页 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.1 Summary of Mechanical Vibration1.1.1

2、 Summary of Mechanical Vibration Vibrating Phenomena in the World Vibration are found in many branches of sc i e nc e a nd engineering 第2页/共64页 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.1 Summary of Mechanical Vibration1.1.1 Summary of Mechanical Vibration Undesirable vibratio

3、ns： Vehicle; Noise; Machines Earthquake; 第3页/共64页 Useful vibrations： String vibration; harmonic oscillator, resonator; Vibrating road roller; Vibrating feeder; Vibrating forming machine. 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.1 1.1.1 Summary of Mechanical Vibration 第4页/共64页

4、 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.2 Basic Concept1.1.2 Basic Concept Mechanical Vibration ? Research aim ? Vibration is a phenomena that a body or structure oscillates about some specified reference point. Vibration is commonly expressed in terms of frequency , amplit

5、ude and Phase angle. 1. Elimination or suppression of undesirable vibrations 2. Generation of the necessary forms and quantities of useful vibrations 第5页/共64页 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.3 Model of Vibration System1.1.3 Model of Vibration System （集中参数系统）（集中参数系统）

6、（分布参数系统）（分布参数系统） 第6页/共64页 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.4 Clarification of Mechanical 1.1.4 Clarification of Mechanical VibrationsVibrations The least number of mutually independent parameters (coordinates) required to uniquely define a material systems position in

7、 space, time, etc 多自由度系统振动多自由度系统振动 (multiple degree of freedom) 振动振动 第7页/共64页 Chapter 1 Introduction z 多自由度系统振动多自由度系统振动 (multiple degree of freedom) ABAB 第8页/共64页 Chapter 1 Introduction 模型与自由度模型与自由度 (Model and degree of freedom) 第9页/共64页 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1

8、.1.4 Clarification of Mechanical 1.1.4 Clarification of Mechanical VibrationsVibrations (no force) 强迫振动强迫振动 (forced vibration) (external force) the periodic motion occurring when an elastic system is displaced from its equilibrium position; the vibration resulting from the application of an external

9、 force； 第10页/共64页 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.4 Clarification of Mechanical 1.1.4 Clarification of Mechanical VibrationsVibrations ;周期振动周期振动 (periodic vibration) 振动振动 振动振动 Harmonic vibration Oscillations in which motion is periodic with time in the form of a sine

10、 curve. Periodic vibration An oscillatory motion whose amplitude pattern repeats after fixed increments of time. Transient vibration Temporarily sustained vibration of a mechanical system. It may consist of forced vibration. Random vibration A vibration whose instantaneous amplitude is not specified

11、 at any instant of time. 第11页/共64页 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.4 Clarification of Mechanical 1.1.4 Clarification of Mechanical VibrationsVibrations Differential Equation 非线性振动非线性振动 (nonlinear vibration) Linear Vibration Linear differential equation ; (superpositi

12、on) Nonlinear vibration Nonlinear differential equation Bifurcation & Chaos 第12页/共64页 Vibration System ExcitationResponse Vibration analysis or Response analysis Vibration System ExcitationResponse Vibration environment prediction Vibration System ExcitationResponse Vibration design or System identi

13、fication 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.5 Problems of Mechanical Vibration and 1.1.5 Problems of Mechanical Vibration and Solving Methods Solving Methods 第13页/共64页 1. 1 Mechanical Vibration and Control Chapter 1 Introduction vTheoretical analysis 1.1.5 Problems of M

14、echanical Vibration and 1.1.5 Problems of Mechanical Vibration and Solving Methods Solving Methods R e a l system Mechanics principle D.E. Numerical solution Analytical solution Computer simulation Mathematical tools V i b r a t i o n characteristics 第14页/共64页 vExperiment Vibration monitoring, testi

15、ng, and experimentation are important as well in the design, implementation, maintenance, and repair of engineering systems. Chapter 1 Introduction All these are important topics of study in the field of vibration engineering, 1.1.5 Problems of Mechanical Vibration and 1.1.5 Problems of Mechanical V

16、ibration and Solving Methods Solving Methods 1. 1 Mechanical Vibration and Control 第15页/共64页 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.6 Mechanical Vibration Control Methods1.1.6 Mechanical Vibration Control 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。 第16页/共64页 1. 1 Mechani

17、cal Vibration and Control Chapter 1 Introduction 1.1.6 Mechanical Vibration Control Methods1.1.6 Mechanical Vibration Control Methods 避免共振；减振与隔振。避免共振；减振与隔振。 第17页/共64页 1. 2 Mechanical Noise and Control Chapter 1 Introduction 1.2.1 Sound and Noise1.2.1 Sound and Noise Sound Wave is any disturbance tha

18、t is propagated in an elastic medium Sound Source is an object that caused vibration of medium particles Sound Field is a space where the sound wave exists 第18页/共64页 1. 2 Mechanical Noise and Control Chapter 1 Introduction 1.2.1 Sound and Noise1.2.1 Sound and Noise Noise is any unwanted sound percei

19、ved by the hearing sense of a human is a mixture of sound waves with different frequencies and strengths 第19页/共64页 1. 2 Mechanical Noise and Control Chapter 1 Introduction 1.2.2 Noise Effects1.2.2 Noise Effects Hearing and Health Excessive noise can impair hearing, may also put stress on the heart,

20、the circulatory system, and other parts of the body Technical Standards For example, the pass-by noise national standards for cars, 84 dB(A) (1979), 78 dB(A) (1985), 74 dB(A) (2006). Military Vehicles Require High stealth capabilities Quiet working and living environment 第20页/共64页 1. 2 Mechanical No

21、ise and Control Chapter 1 Introduction 1.2.3 Clarifications of Mechanical Noise1.2.3 Clarifications of Mechanical Noise 流体动力性噪声流体动力性噪声 (Fluid dynamic noise) 空气噪声空气噪声 (Air-borne noise) 第21页/共64页 1. 2 Mechanical Noise and Control Chapter 1 Introduction 1.2.4 Methods of Mechanical Noise Control1.2.4 Me

22、thods 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 第22页/共64页 第23页/共64页 Chapter 2 Vibration of Single-Degree-of-Freedom System (

23、SDOF) 2. 1 Differential Equation of Vibration 2. 2 Free Vibration 2. 3 Forced Vibration 2. 4 Vibration Isolation Outline: 第24页/共64页 2. 1 Differential Equation of Vibration 第25页/共64页 1. piston 2. connecting rod 3. crankshaft 4. flywheel 5. intermediate shaft 6. screw propeller 2. 1 Differential Equat

24、ion of Vibration 第26页/共64页 2.1.1.1 2.1.1.1 Discretization of physical system Mass element Spring elementDamping element 2.1.1 Mechanical Model of Physical System 2. 1 Differential Equation of Vibration 第27页/共64页 2.1.1.1 2.1.1.1 Discretization of physical system 2.1.1 Mechanical Model of Physical Sys

25、tem 2. 1 Differential Equation of Vibration 第28页/共64页 2.1.1.1 2.1.1.1 Discretization of physical system 2.1.1 Mechanical Model of Physical System 2. 1 Differential Equation of Vibration 第29页/共64页 Mass element 质量元件质量元件 xmFm Translation平移平移： Force力力, mass质量质量 & acceleration加速度加速度 Units量纲量纲: N、kg、m/s 2

26、。 JTm Rotation旋转旋转： Moment力矩力矩, moment of inertia转动惯量转动惯量 & angular acceleration角加速度角加速度 Units量纲量纲: Nm、kg m 2、rad / s 2 2.1.1.2 2.1.1.2 Discretized mechanical system 2.1.1 Mechanical Model of Physical System 2. 1 Differential Equation of Vibration 第30页/共64页 xkFs ts kT Spring (elastic) element 弹性元件弹性

27、元件 Force力力, stiffness刚度刚度 &displacement位移位移Units量纲量纲: N, N/m & m Moment力矩力矩, torsion stiffness扭转刚度扭转刚度 & angle角位移角位移Units量纲量纲: Nm, Nm/rad & rad Translation平移平移： Rotation旋转旋转： 2.1.1.2 2.1.1.2 Discretized mechanical system 2.1.1 Mechanical Model of Physical System 2. 1 Differential Equation of Vibrati

28、on 第31页/共64页 xcFd td cT Damping element 阻尼元件阻尼元件 Force力力, damping coefficient阻尼系数阻尼系数& velocity速度速度Units量纲量纲: N, Ns/m & m/s 。 Moment力矩力矩, torsion damping coefficient扭转阻尼系数扭转阻尼系数& angular velocity角速度角速度 Units量纲量纲: Nm, Nms/rad & rad/s Translation平移平移： Rotation旋转旋转： 2.1.1.2 2.1.1.2 Discretized mechanic

29、al system 2.1.1 Mechanical Model of Physical System 2. 1 Differential Equation of Vibration 第32页/共64页 (1) Force method 2.1.2 Methods to Establish Differential Equation Steps： 1. Generalized coordinate 建立广义坐标建立广义坐标 2. Draw a diagram of equilibrium of forces of the mass element 作质量元件的隔离体受力分析图作质量元件的隔离体

30、受力分析图 3. Normal form of the vibration equation 建立振动微分方程并建立振动微分方程并 整理成标准的形式整理成标准的形式 2. 1 Differential Equation of Vibration 第33页/共64页 (1) Force method Example 2-2 SDOF damping system Generalized coordinate .建立广义建立广义 坐标坐标 (direction方向方向,origin原点原点) Mechanics principle 力学定律力学定律 xmtFmgxcxk )()( )(tFkxxc

31、xm 2. 1 Differential Equation of Vibration 2.1.2 Methods to Establish Differential Equation Equilibrium of forces at the mass element质量受力的平衡质量受力的平衡 第34页/共64页 single pendulum Generalized coordinate . (direction,origin) Equilibrium of moments at the joint DAlembert Principle 0sin 2 lgmlm sin 0）（lg (1)

32、 Force method Example 2-3 2. 1 Differential Equation of Vibration 2.1.2 Methods to Establish Differential Equation 第35页/共64页 Multiple 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

33、Newton 2nd law for m1 and m2 111 m aRk a 222 22m aRk a 第36页/共64页 (1) Force method Example 2-4 2. 1 Differential Equation of Vibration 2.1.2 Methods to Establish Differential Equation Moment law for m3 0 2 2 3 321 2JakaRaR where 2 30 amJ 222222 1 1231234 4420m am am ak ak ak a 0 tee kJ or 第37页/共64页 0

34、d/dtPUV）（ 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 2 1 xmT 2 00 111 1 2 nnn xx iiiii iii UF dxk x dxk x 2. Kinetic energy V, potential energy U & dissipa

35、tion energy P 2 00 11 nn xt iiii ii PC x dxC x dt 第38页/共64页 (2) Energy method Example 2-5 ： 2. 1 Differential Equation of Vibration 2.1.2 Methods to Establish Differential Equation 1. Generalized coordinate. 2. Kinetic energy 动能动能T、potential energy 势能势能U 3. Using principle of conservation of energy

36、2 00 2 1 kxkxdxFdxU xx 0 kxxmUT 代入上式，得、将 0)(,UT dt d UT所以有常数 x x F m o 2 2 1 xmT 第39页/共64页 Multiple Mass System Generalized coordinate (direction,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 第40页/共64页 Kine

37、tic energy V Potential energy U Dissipation energy P Using principle of conservation of energy 22 3 22 2 22 1 2 1 2 2 1 amamamV 22 3 22 2 22 1 4 9 2 1 4 2 1 2 1 akakakU 0P 0) 4 1 24( 4 2 3 2 2 2 1 2 3 2 2 2 1 akakak amamam）（ Example 2-6 (2) Energy method 2. 1 Differential Equation of Vibration 2.1.2

38、 Methods to Establish Differential Equation 第41页/共64页 Multi-mass (or spring, damping) elements General form of vibration equation for SDOF system )( eee tFxkxcxm )( e t e te tTkcJ Translation： Rotation： 2. 1 Differential Equation of Vibration 2.1.3 Equivalent System Single-mass (or spring, damping)

39、element 第42页/共64页 Equivalent stiffness x F k x e xkF n i ix )( 1 n i i k 1 2. 1 Differential Equation of Vibration 2.1.3 Equivalent System (1) Equivalent stiffness Methods： 1 Definition of stiffness。 2 Potential energy 第43页/共64页 Series Springs Series Springs Equivalent stiffness x F k x e n i i x n

40、i i x n i i k F k F xx 111 1 n i i k 1 1 1 2. 1 Differential Equation of Vibration 2.1.3 Equivalent System 第44页/共64页 n i i cc 1 e n ii cc 1e 11 Parallel systemSeries system (2) Equivalent damping 2. 1 Differential Equation of Vibration 2.1.3 Equivalent System 第45页/共64页 Example 2-7 Equivalent mass to

41、 A point Spring-lever-mass system Kinetic Energy (original system) 2 2 2 4 2 1 2 2 1 2 1 xmml l x mxmV baba Kinetic Energy (equivalent system) 2 ee 2 1 xmV VV eba mmm4 e (3) Equivalent mass (kinetic energy equivalence) 2. 1 Differential Equation of Vibration 2.1.3 Equivalent System 第46页/共64页 Problem

42、s 2-2, 2-3, 2-4, 2-5, 2-6, 2-9, 2-12 Home Works Pages 41&42 第47页/共64页 第48页/共64页 kxxm 0 kxx m 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。 0lx x k m O kx N mg Let ，we have m k n 2 0 2 xx n tBtAx tBtAx nnn n n n sincos cossin The solution of the equation above is 2. 2 Free Vibration 2.2.1 Undamped S

43、ystem 第49页/共64页 Assuming the initial condition to be 设初始条件为 0l 0 x x k m O The solution equation under the initial condition will be 则在此初始条件下的响应为 00 )0(,)0(xxxx txt x x n n n cossin 0 0 2. 2 Free Vibration 2.2.1 Undamped System 2 n0 2 0 )/(xxR 0tanarc 0tanarc 0 n0 0 0 n0 0 x x x x x x cos() n xRtx o

44、 x R n n o t 第50页/共64页 Or 或 Here 式中 )sin(tXx n 0 0 1 2 1 22 0 )( 0 x x tg，x x X n n f T X n Circular natural frequency 圆频率 Amplitude 振幅 Phase angle 相角 Period 周期 Natural frequency 频率 n T/2 )2/( n f 2. 2 Free Vibration 2.2.1 Undamped System A systems period and frequency are determined by its p h y s

45、i c a l properties. mk / n 第51页/共64页 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 )sin(tXx n )2/sin(tXx nn )sin( 2 tXx n n 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 Und

46、amped System 第52页/共64页 From the equations of the amplitude and phase angle 0 0 1 2 1 22 0 )( 0 x x tg，x x X n n 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

47、 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 Undamped System 第53页/共64页 |the static displacement |The energy method |the equation of motion )(cos n tAx )(cos 2 1 2 1 n 222 tAkxkU )(sin 2 1 2 1 n 22 n 22 tAmxmV maxmax VU m k n 0 2 n xx s g mg kg m k n The natu

48、ral frequency of the undamped system can be determined by Vibration characteristics 2.2 Free Vibration 2.2.1 Undamped System 0kxx m 第54页/共64页 kg1 1 m m/N100 1 k kg4 2 m m/N100 2 k kg1 3 m m/N400 3 k Initial displacement 10-3m Initial velocity 10-2m/s Example 2-8 What is the free vibration responses of the following systems? 2. 2 Free Vibration 2.2.1 Undamped System 第55页/共64页 )(cos)( n tRtx ,)/( 2 n0 2 0 xxR 0tanarc 0tanarc 0 n0 0 0 n0 0 x x x x x x , n