Theoretical Mechanics Chapter 18: Mechanical Vibrations
1 Theoretical Mechanics
理论力学 第十八章动
2
Dynamic Vibrations are common phenomena in everyday life and in engineering practice. Such as the swinging of a clock pendulum, the bumping of a notors, and the quake of buildings caused by an earthquake. 1. Vibrations are the back and forth movements of a system around its equilibrium position. 2. Advantages and disadvantages of vibrations: Vibrating feeder, vibrating screen, vibrating pile driver extractor, for example, are advantageous applications. But vibrations induce friction loss, affect intensity, make noise, have bad effects on working conditions, consume unnecessary energy and reduce the precision of a machine etc. 3. The aim of the study of vibrations is the elimination or reduction of harmful oscillations, or the helpful use of them for special purposes. 3
3 Vibrations are common phenomena in everyday life and in engineering practice. Such as the swinging of a clock pendulum, the bumping of a traveling car, the vibrations of working machine parts or motors, and the quake of buildings caused by an earthquake. 3. The aim of the study of vibrations is the elimination or reduction of harmful oscillations, or the helpful use of them for special purposes. 2. Advantages and disadvantages of vibrations: Vibrating feeder, vibrating screen, vibrating pile driver extractor, for example, are advantageous applications. But vibrations induce friction loss, affect intensity, make noise, have bad effects on working conditions, consume unnecessary energy and reduce the precision of a machine etc. 1. Vibrations are the back and forth movements of a system around its equilibrium position
学 振动是日常生活和工程实际中常见的现象。 例如:钟摆的往复摆动汽车行驶时的颠簸,电动机、机 床等工作时的振动,以及地震时引起的建筑物的振动等。 1所谓振动就是系统在平衡位置附近作往复运动。 2.振动的利弊: 利:振动给料机弊:磨损,减少寿命,影响强度 振动筛 引起噪声,影响劳动条件 振动沉拔桩机等消耗能量,降低精度等。 3.研究振动的目的:消除或减小有害的振动,充分利用振动 为人类服务
4 振动是日常生活和工程实际中常见的现象。 例如：钟摆的往复摆动,汽车行驶时的颠簸，电动机、机 床等工作时的振动，以及地震时引起的建筑物的振动等。 利：振动给料机 弊：磨损，减少寿命，影响强度 振动筛 引起噪声，影响劳动条件 振动沉拔桩机等 消耗能量，降低精度等。 3. 研究振动的目的：消除或减小有害的振动，充分利用振动 为人类服务。 2. 振动的利弊： 1. 所谓振动就是系统在平衡位置附近作往复运动
Dynamic 4. Classification of vibrations: Vibrations of systems with one degree of freedom According to the number of degrees of freedom of a vibrating Vibrations of systems with more than one degree of system they can be classified into freedom and Vibrations of elastic bodies According to the cause of the vibrations they can be classified into free vibrations including undamped free vibrations and damped free vibrations including undamped forced vibrations and forced vibrations damped forced vibrations self-excited forced vibrations The present chapter discusses mainly free vibrations and forced vibrations of systems with one degree of freedom
5 The present chapter discusses mainly free vibrations and forced vibrations of systems with one degree of freedom. 4. Classification of vibrations: Vibrations of systems with one degree of freedom Vibrations of systems with more than one degree of freedom and Vibrations of elastic bodies According to the number of degrees of freedom of a vibrating system they can be classified into According to the cause of the vibrations they can be classified into free vibrations including undamped free vibrations and damped free vibrations forced vibrations including undamped forced vibrations and damped forced vibrations self-excited forced vibrations
学 4振动的分类 单自由度系统的振动 按振动系统的自由度分类多自由度系统的振动 弹性体的振动 按振动产生的原因分类 自由振动:无阻尼的自由振动 有阻尼的自由振动,衰减振动 强迫振动:无阻尼的强迫振动 有阻尼的强迫振动 自激振动 本章重点讨论单自由度系统的自由振动和强迫振动
6 4. 振动的分类： 单自由度系统的振动 按振动系统的自由度分类 多自由度系统的振动 弹性体的振动 按振动产生的原因分类： 自由振动： 无阻尼的自由振动 有阻尼的自由振动，衰减振动 强迫振动： 无阻尼的强迫振动 有阻尼的强迫振动 自激振动 本章重点讨论单自由度系统的自由振动和强迫振动
Chapter 18: Mechanical vibrations 818-1 Undamped free vibration of a system with one degree of freedom 818-2 Methods of determination of the natural frequency of a system 818-3 Damped free vibration of a system with one degree of freedom 818-4 Undamped forced vibration of a system with one degree of freedom 818-5 Damped forced vibration of a system with one degree of freedom 818-6 The concepts of critical speed of rotation. vibration reduction and vibration isolation
7 §18–1 Undamped free vibration of a system with one degree of freedom §18–2 Methods of determination of the natural frequency of a system §18–3 Damped free vibration of a system with one degree of freedom §18–4 Undamped forced vibration of a system with one degree of freedom §18–5 Damped forced vibration of a system with one degree of freedom §18–6 The concepts of critical speed of rotation, vibration reduction and vibration isolation Chapter 18: Mechanical vibrations
第十八章机械振动基础 §18-1单自由度系统无阻尼自由振动 四§18-2求系统固有频率的方法 §18-3单自由度系统的有阻尼自由振动 §184单自由度系统的无阻尼强迫振动 §185单自由度系统的有阻尼强迫振动 §18-6临界转速·减振与隔振的概念
8 §18–1 单自由度系统无阻尼自由振动 §18–2 求系统固有频率的方法 §18–3 单自由度系统的有阻尼自由振动 §18–4 单自由度系统的无阻尼强迫振动 §18–5 单自由度系统的有阻尼强迫振动 §18–6 临界转速 · 减振与隔振的概念 第十八章 机械振动基础
Dynarnics 818-1 Undamped free vibration of a system with one degree of freedom 1. Concept of free vibration motor O 基础 Elastic foundation
9 §18-1 Undamped free vibration of a system with one degree of freedom 1.Concept of free vibration motor Elastic foundation
力单 §18-1单自由度系统无阻尼自由振动 自由振动的概念: 电动机 基础 弹性地基 10
10 §18-1 单自由度系统无阻尼自由振动 一、自由振动的概念：