hi,小慕
Mechanics of Vibration
第9次开课
开课时间: 2025年03月01日 ~ 2025年06月30日
学时安排: 3-5小时每周
进行至第5周,共18周 已有 17 人参加
立即参加
课程详情
课程评价(13)
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—— 课程团队
课程概述

Vibration phenomenon is ubiquitous and one of the most common phenomena in nature. The vibration in engineering can be found everywhere, such as the vibration of building structures and bridges under wind or seismic loads, vibration of mechanical systems during operation, vibration of cutting tools, flutter of airplane wings, vibration of various impact events and so on. Although vibration phenomenon has its own characteristics, it has the same objective law, so it is possible to establish a unified theory to study. 


The main task of vibration mechanics course is to study the dynamic behavior of linear system, analyze the natural vibration characteristics of the system and the basic theory and calculation method of system response analysis under deterministic (or stochastic) dynamic load. The purpose of teaching is to enable students to master the basic principles of vibration mechanics and the methods of solving problems on the basis of learning theoretical mechanics and material mechanics. Establishing the concept of structural or system dynamic characteristics; Master the modeling, solution and result analysis methods of linear discrete and continuous elastomer systems; To have a deep understanding of vibration theory, analysis method and its preliminary application in engineering. It lays a necessary mechanical foundation for the research, engineering design and technical development of mechanical problems in engineering field.

课程大纲
Introduction
课时目标:Describe briefly the history of vibration; Indicate the importance of study of vibration; Give various classifications of vibration; State the steps involved in vibration analysis.
1.1 Brief History of the Study of Vibration
1.2 Importance of the Study of Vibration and Basic Concepts
1.3 Classification of Vibration and Vibration Analysis Procedure
Free Vibration of Single-Degree-of-Freedom
课时目标:Derive the equation of motion of a single-degree-of-freedom system; Linearize the nonlinear equation of motion; Solve a spring-mass-damper system for different types of free-vibration response; Compute the natural frequency, damped frequency, logarithmic decrement, and time constant.
2.1 Free Vibration of an Undamped System PartⅠ
2.2 Free Vibration of an Undamped System Part Ⅱ
2.3 Energy Method and Rayleigh Method
2.4 Free Vibration with Viscous Damping Ⅰ
2.5 Free Vibration with Viscous Damping Ⅱ
Harmonically Excited Vibration of SDOF systems
课时目标:Find the responses of undamped and viscously damped single-degree-of-freedom systems subjected to different types of harmonic force; Understand the variations of magnification factor and phase angles with the frequency of excitation and the phenomena of resonance and beats.
3.1 Harmonically Excited Vibration of SDOF Systems
3.2 Response of an Undamped System Under Harmonic Force
3.3 Response of a Damped System Under Harmonic Force
3.4 Base Excitation
3.5 Rotating Unbalance
3.6 Vibration Measurement Instrument
Vibration Under General Forcing Condition
课时目标:Find the response of SDOF systems subjected to general periodic forces using the Fourier series; Use the method of convolution or Duhamel integral to solve vibration problems of systems subjected to arbitrary forces
4.1 Response Under a General Periodic Force
4.2 Response Under a Nonperiodic Force
Vibration of Two-Degree-of-Freedom (2DOF) Systems
课时目标:Formulate the equations of motion of two-degree-of-freedom systems; Compute the eigenvalues or natural frequencies of vibration and the modal vectors; Determine the free-vibration solution using the known initial conditions; Determine the forced-vibration solutions under harmonic forces; Understand the concepts of design techniques for undamped and damped vibration absorbers
5.1 Introduction
5.2 Equations of Motion for Forced Vibration
5.3 Natural Frequencies and Mode Shapes
5.4 Free Vibration Analysis of an Undamped System
5.5 Coordinate Coupling and Principal Coordinates
5.6 Forced-Vibration Analysis
5.7 Vibration AbsorberⅠ
5.8 Vibration Absorber Ⅱ
Vibration of Multi-Degree-of-Freedom (MDOF) Systems
课时目标:Formulate the equations of motion of multi-DOF systems; Express the equation of motion in matrix form; Find the natural frequencies of vibration and modal vectors; Determine the free- and forced-vibration response of undamped systems using modal analysis; Use proportional damping to find the response damped systems.
6.1 Modelling and Equations of MDOF systemsⅠ
6.2 Modelling and Equations of MDOF systemsⅡ
6.3 Influence CoefficientsⅠ
6.4 Influence CoefficientsⅡ
6.5 Potential and Kinetic Energy Expressions in Matrix Form
6.6 Eigenvalue ProblemⅠ
6.7 Eigenvalue ProblemⅡ
6.8 Unrestrained Systems
6.9 Free Vibration of Undamped Systems
6.10 Forced Vibration of MDOF Systems
Vibration of Continuous Systems
课时目标:Derive the equation of motion of a continuous system from the free-body diagram; Find the natural frequencies and mode shapes of the system; Determine the free-vibration solution using a linear superposition of the mode shapes and the initial conditions; Find the free-vibration solutions of string, bar and beam.
7.1 Transverse Vibration of a String of Cable
7.2 Longitudinal Vibration of a Bar or Rod
7.3 Lateral Vibration of Beams
展开全部
预备知识

Ø Theoretical mechanics


Ø Mechanics of materials


Ø Advanced mathematics or engineering mathematics analysis


Ø Linear algebra


Ø Ordinary differential equations

参考资料

Singiresu S. Rao. Mechanical Vibrations (5th Edition). Pearson. 

William T. Thomson. Theory of Vibration with Applications (5th Edition). CRC Press. 

Sinha, Alok. Vibration of Mechanical Systems. Cambridge University Press. 

S. Graham Kelly. Mechanical Vibrations: Theory and Applications, Cengage Learning.

刘延柱,陈立群,陈文良 编著. 《振动力学》(第3版). 高等教育出版社,2019.

刘习军、贾启芬、张素侠主编,《振动理论及工程应用》,第二版,机械工业出版社,2017年.

东南大学
1 位授课老师
Wenjie WANG

Wenjie WANG

副教授

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