機(jī)械振動噪聲與控制PPT學(xué)習(xí)教案

1、會計(jì)學(xué)1 機(jī)械振動噪聲與控制機(jī)械振動噪聲與控制 2. R.F. Barron, Industrial Noise Control and Acoustics, Marcel Dekker, 2003 3. 鄭兆昌主編， 機(jī)械振動（上冊），機(jī)械工業(yè)出版社， 1980 4. 商大中，動力分析基礎(chǔ)，哈爾濱工程大學(xué)出版社， 1999 5. 季文美，機(jī)械振動，科學(xué)出版社， 1985 第1頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁

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頁/共64頁 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.3 Model of Vibration System1.1.3 Model of Vibration System （集中參數(shù)系統(tǒng)）（集中參數(shù)系統(tǒng)）

6、（分布參數(shù)系統(tǒng)）（分布參數(shù)系統(tǒng)） 第6頁/共64頁 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 多自由度系統(tǒng)振動多自由度系統(tǒng)振動 (multiple degree of freedom) 振動振動 第7頁/共64頁 Chapter 1 Introduction z 多自由度系統(tǒng)振動多自由度系統(tǒng)振動 (multiple degree of freedom) ABAB 第8頁/共64頁 Chapter 1 Introduction 模型與自由度模型與自由度 (Model and degree of freedom) 第9頁/共64頁 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) 強(qiáng)迫振動強(qiáng)迫振動 (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頁/共64頁 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.4 Clarification of Mechanical 1.1.4 Clarification of Mechanical VibrationsVibrations ;周期振動周期振動 (periodic vibration) 振動振動 振動振動 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頁/共64頁 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.4 Clarification of Mechanical 1.1.4 Clarification of Mechanical VibrationsVibrations Differential Equation 非線性振動非線性振動 (nonlinear vibration) Linear Vibration Linear differential equation ; (superpositi

12、on) Nonlinear vibration Nonlinear differential equation Bifurcation & Chaos 第12頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁 1. 1 Mechanical Vibration and Control Chapter 1 Introduction 1.1.6 Mechanical Vibration Control Methods1.1.6 Mechanical Vibration Control Methods 壓榨機(jī)的飛輪和傳動帶 的保護(hù)罩是主要的噪 聲源。保護(hù)罩用實(shí)體 金屬薄片制成。 第16頁/共64頁 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；減振與隔振。避免共振；減振與隔振。 第17頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁 1. 2 Mechanical No

21、ise and Control Chapter 1 Introduction 1.2.3 Clarifications of Mechanical Noise1.2.3 Clarifications of Mechanical Noise 流體動力性噪聲流體動力性噪聲 (Fluid dynamic noise) 空氣噪聲空氣噪聲 (Air-borne noise) 第21頁/共64頁 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頁/共64頁 第23頁/共64頁 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頁/共64頁 2. 1 Differential Equation of Vibration 第25頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁 Mass element 質(zhì)量元件質(zhì)量元件 xmFm Translation平移平移： Force力力, mass質(zhì)量質(zhì)量 & acceleration加速度加速度 Units量綱量綱: N、kg、m/s 2

26、。 JTm Rotation旋轉(zhuǎn)旋轉(zhuǎn)： Moment力矩力矩, moment of inertia轉(zhuǎn)動慣量轉(zhuǎn)動慣量 & angular acceleration角加速度角加速度 Units量綱量綱: 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頁/共64頁 xkFs ts kT Spring (elastic) element 彈性元件彈性

27、元件 Force力力, stiffness剛度剛度 &displacement位移位移Units量綱量綱: N, N/m & m Moment力矩力矩, torsion stiffness扭轉(zhuǎn)剛度扭轉(zhuǎn)剛度 & angle角位移角位移Units量綱量綱: Nm, Nm/rad & rad Translation平移平移： Rotation旋轉(zhuǎn)旋轉(zhuǎn)： 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頁/共64頁 xcFd td cT Damping element 阻尼元件阻尼元件 Force力力, damping coefficient阻尼系數(shù)阻尼系數(shù)& velocity速度速度Units量綱量綱: N, Ns/m & m/s 。 Moment力矩力矩, torsion damping coefficient扭轉(zhuǎn)阻尼系數(shù)扭轉(zhuǎn)阻尼系數(shù)& angular velocity角速度角速度 Units量綱量綱: Nm, Nms/rad & rad/s Translation平移平移： Rotation旋轉(zhuǎn)旋轉(zhuǎn)： 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頁/共64頁 (1) Force method 2.1.2 Methods to Establish Differential Equation Steps： 1. Generalized coordinate 建立廣義坐標(biāo)建立廣義坐標(biāo) 2. Draw a diagram of equilibrium of forces of the mass element 作質(zhì)量元件的隔離體受力分析圖作質(zhì)量元件的隔離體

30、受力分析圖 3. Normal form of the vibration equation 建立振動微分方程并建立振動微分方程并 整理成標(biāo)準(zhǔn)的形式整理成標(biāo)準(zhǔn)的形式 2. 1 Differential Equation of Vibration 第33頁/共64頁 (1) Force method Example 2-2 SDOF damping system Generalized coordinate .建立廣義建立廣義 坐標(biāo)坐標(biāo) (direction方向方向,origin原點(diǎn)原點(diǎn)) Mechanics principle 力學(xué)定律力學(xué)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質(zhì)量受力的平衡質(zhì)量受力的平衡 第34頁/共64頁 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頁/共64頁 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頁/共64頁 (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頁/共64頁 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頁/共64頁 (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 動能動能T、potential energy 勢能勢能U 3. Using principle of conservation of energy

36、2 00 2 1 kxkxdxFdxU xx 0 kxxmUT 代入上式，得、將 0)(,UT dt d UT所以有常數(shù) x x F m o 2 2 1 xmT 第39頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁 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頁/共64頁 Problem

42、s 2-2, 2-3, 2-4, 2-5, 2-6, 2-9, 2-12 Home Works Pages 41&42 第47頁/共64頁 第48頁/共64頁 kxxm 0 kxx m 對如右圖所示系統(tǒng)，可 建立坐標(biāo)系x，畫出質(zhì)量m的 受力隔離體圖，利用牛頓定 律列出運(yùn)動方程。 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頁/共64頁 Assuming the initial condition to be 設(shè)初始條件為 0l 0 x x k m O The solution equation under the initial condition will be 則在此初始條件下的響應(yīng)為 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頁/共64頁 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 圓頻率 Amplitude 振幅 Phase angle 相角 Period 周期 Natural frequency 頻率 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頁/共64頁 Discussion 討 論 The displacement,velocity and acceleration of the system are as followed 系統(tǒng)的位移、速度、加速度分別為 )sin(tXx n )2/sin(tXx nn )sin( 2 tXx n n They are all harmonic function 可見系統(tǒng)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. 2 Free Vibration 2.2.1 Und

46、amped System 第52頁/共64頁 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. 系統(tǒng)振動的振幅和相角都決定于初始條件，這正是振動系統(tǒng)自由振動 的特性。 But a systems period and frequency are

47、 determined by its physical properties. 但系統(tǒng)的周期和頻率則取決于它的物理特性。 2. 2 Free Vibration 2.2.1 Undamped System 第53頁/共64頁 |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頁/共64頁 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頁/共64頁 )(cos)( n tRtx ,)/( 2 n0 2 0 xxR 0tanarc 0tanarc 0 n0 0 0 n0 0 x x x x x x , n