哈工大课件机械系统动力学Dynamics of Mechanical System-ch1

机械系统动力学机电工程学院 机械设计系

Chen Zhaobo (陈照波)Tel: 86412057 E-mail: chenzb@http://www.77cn.com.cn 机械楼一楼1020室

参考书1. 闻邦椿等《机械振动理论及应用》 高等教育出版社

2. 胡海岩 《机械振动基础》 北京航空航天大学出版社3. 师汉民 《机械振动系统》 华中科技大学出版社 4. W. T. Thomson 《振动理论及应用》 清华大学出版社

………

考核办法—累加式1. 大作业1 10%

2. 大作业23. 平时表现 4. 期终考试

10%10% 70%

Preface

What is dynamics?Dynamics focuses on understanding why objects move the way they do.

Dynamics = Kinematics + KineticsKinematics is the study of the motion of point masses or rigid bodies. Kinetics is the study of the forces which cause and affect motion.

What is mechanical system? Structure

Mechanism

Machine

Development stages of dynamics of mechanical systems: Static analysis Kineto-static analysis Dynamic analysis Elasto-dynamic analysis

Why to study dynamics of mechanical system? Higher speed Higher precision More flexible More complicated

Resonance

When a forcing frequency is equal to a natural frequency

COURSE GOALS:1. To become proficient at modeling vibrating mechanical systems. 2. To perform dynamic analysis such as free and forced response of SDOF and MDOF systems. 3. To understand concepts of modal analysis. 4. To understand concepts in passive and active vibration control systems.

Prerequisites: The most important prerequisite is ordinary differential equations. You should be prepared to review undergraduate differential equations if necessary.

Chapter 1 Single degree of freedom systems

Objectives Recognize a SDOF system Be able to solve the free vibration equation of a SDOF system with and without damping Understand the effect of damping on the system vibration Apply numerical tools to obtain the time response of SDOF system

Single degree of freedom systems When one variable can describe the motion of a structure or a system of bodies, then we may call the system a 1-D system or a single degree of freedom (SDOF) system.

Undamped Spring-Mass System

LUnloaded Spring

k st m x

At equilibrium, k st = mg

Body in equilibrium (at rest)

m

Body in motion

Free Body Diagram

x

k( st + x )

=mg

.. mx

Equations of motionSum forces:

F : mg - k st x m x Rearrange to yield the familiar equation of motion: