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Table of Contents
1 Nonlinear vibration – Gu Zhiping – China Electric Power Press, 2012
Introduction Chapter 1 Conservative System with Single Degree of Freedom 1.1 Example of Conservative System with Single Degree of Freedom 1.2 Qualitative Analysis Method 1.3 Quantitative Analysis Method 1.4 Application of Quantitative and Qualitative Methods Chapter 2 Non-Conservative System with Single Degree of Freedom 2.1 Mechanism of Damping 2.2 Qualitative Analysis 2.3 Approximate Solution 2.4 Unsteady vibration 2.5 Relaxation vibration Chapter 3 Forced vibration of a single-degree-of-freedom system 3.1 System with cubic nonlinearity 3.2 System with square sum cubic nonlinearity 3.3 Self-excited system 3.4 Unsteady vibration 3.5 Non-ideal system Chapter 4 Parameter excitation System 4.1 Analysis example 4.2 Floquet theory 4.3 Single-degree-of-freedom system Chapter 5 Finite-degree-of-freedom system 5.1 Free vibration of system with square nonlinearity 5.2 Forced vibration of system with square nonlinearity 5.3 Average method 5.4 Harmonic linearization method 5.5 Non Examples of discretization of linear continuous systems
2 Liu Yanzhu - vibration mechanics - Higher Education Press -2011
2.1 content
Introduction 0.1 Vibration and Vibration Mechanics 0.2 Classification of Vibration 0.3 Brief History of Development of Vibration Mechanics 0.4 Application of Vibration Mechanics in Engineering Chapter 1 Free Vibration 1.1 Free Vibration of Linear Systems 1.2 Phase Trajectories and Singularities 1.3 Free Vibration of Conservative Systems 1.4 Static Analysis bifurcated free vibration dissipation system 1.5 exercises Chapter forced vibration by forced vibration system of the linear 2.1 2.2 engineering by forced vibration by forced vibration of Nonlinear systems 2.3 2.4 forced vibration Chaos for exercises Chapter III Transient Response 3.1 Time Domain Analysis of Transient Response 3.2 Frequency Domain Analysis of Transient Response 3.3 Response to Random Excitation 3.4 Transient Response Problems in Engineering Exercises Chapter 4 Self-Excited Vibration 4.1 Overview of Self-Excited Vibration 4.2 Limit Cycles and Van der Pol Equation 4.3 Self-excited vibration in engineering 4.4 Relaxation vibration and dynamic bifurcation Exercises Chapter 5 Vibration of multi-freedom systems 5.1 Dynamic equations of multi-freedom systems 5.2 Free vibration of 5.3 The zero root sum of frequency equations Re-root situation 5.4 Response of multi-degree-of-freedom system 5.5 Damped multi-degree-of-freedom system 5.6 Nonlinear multi-degree-of-freedom system Exercises Chapter 6 Approximate Calculation of Multi-degree-of-freedom System Vibration 6.1 Dunkley Method 6.2 Rayleigh Method 6.3 Ritz Method 6.4 Matrix Iteration Method 6.5 Subspace Iteration Method Exercises Chapter 7 Vibration of Continuous Systems 7.1 Vibration of Strings and Rods 7.2 Bending Vibration of Beams 7.3 Special Problems of Beam Vibration 7.4 Vibration of Membranes and Plates 7.5 Energy Principles and Dynamic Equations Problem Chapter 8 Vibration of Continuous Systems Approximate calculation method 8.1 Concentrated mass method 8.2 Energy principle and Rayleigh quotient 8.3 Hypothetical modal method 8.4 Weighted residual method 8.5 Transfer matrix method 8.6 Finite element method Exercises Appendix Laplace transform table Exercise answers References Index Translation of foreign names Chart
2.2 description
The first edition is a course material for the 21st century and won the first prize in the textbook category of the 2000 Natural Science Award of Chinese Universities. The first edition features high starting points, linear and nonlinear vibrations incorporated into a unified theoretical system, and attention to reflect the results of modern research. The second edition aims at the teaching of undergraduates, and deletes some of the content that is aimed at improving the teaching requirements of graduate students. The linear vibration part supplements the frequency domain analysis method and energy method, appropriately adds new content about the continuous system vibration, strengthens the theoretical basis of the approximation method and the description of error estimation, making the theory more complete and systematic. At the same time, keep the simple analysis of the common nonlinear vibration problems in the project in the original textbook in a simple and easy way, as well as the basic knowledge of random vibration and chaotic vibration. Examples and exercises are supplemented as appropriate. "Vibration Mechanics (Second Edition)" systematically discusses the basic theory and analysis methods of mechanical vibration. The introduction describes the overview and brief history of vibration mechanics. The text is divided into 8 chapters. Chapters 1, 2, and 3 discuss the free vibration, forced vibration, and transient response of the single-degree-of-freedom system. Chapter 4 describes the self-excited vibration. Chapters 5 and 6 discuss the vibration and Approximate calculation methods. Chapters 7 and 8 discuss continuous system vibration and approximate calculation methods. Each chapter is accompanied by exercises and answers. "Vibration Mechanics (Second Edition)" can be used as a textbook for engineering mechanics, mechanical engineering, aeronautical engineering and civil engineering, as well as a reference book for engineering and technical personnel engaged in work related to mechanical vibration.
2.3 authors intro
Liu Yanzhu, born in 1936. In 1959 graduated from the Tsinghua University Engineering Mechanics Research Class. He studied at Moscow University from 1960 to 1962. From 1962 to 1973, he taught at the Department of Engineering Mechanics of Tsinghua University. He taught in the Department of Engineering Mechanics of Shanghai Jiaotong University in 1973. He has served as professor, doctoral tutor, and director of the Institute of Engineering Mechanics. Retired in 2006. He is currently an honorary director of the Chinese Society of Mechanics, a member of the Professional Committee on the History and Methodology of Mechanics, and the Deputy Editor-in-Chief of Mechanics and Practice. His research fields include gyro mechanics, multi-body dynamics, and nonlinear dynamics. Author of "Gyro Mechanics", "Electrostatic Gyroscope Dynamics", "Spacecraft Attitude Dynamics", "Multi-rigid Body System Dynamics", "Theoretical Mechanics", "Advanced Dynamics", "Vibration Mechanics", "Non-linearity" "Dynamics", "Nonlinear Vibration", "Liquid Filling System Dynamics", "Nonlinear Mechanics of Elastic Thin Rods", "Rigid Body Dynamics Theory and Application" and other works. Won the fourth prize of the National Natural Science Award in 1987, the second prize of four scientific and technological progress awards of the Ministry of Education and Shanghai, the first prize of two excellent teaching materials and the three second prizes. Chen Liqun, born in 1963. In 1999, he obtained a Ph.D. from the Engineering Mechanics Department of Shanghai Jiaotong University. From 1997 to 1999, he was a postdoctoral researcher at Shanghai University in Shanghai Applied Mathematics and Mechanics. He taught at the Department of Mechanics of Shanghai University in 1999. He is currently a Distinguished Professor and Doctoral Supervisor of the "Changjiang Scholar" of the Ministry of Education. He is also the deputy director of the Popular Science Working Committee of the Chinese Society of Mechanics, and a member of the Professional Committee of Dynamics and Control. His research areas include nonlinear dynamics, vibration analysis and control. Author of "Vibration Mechanics", "Nonlinear Dynamics", "Nonlinear Vibration" and "Theoretical Mechanics". Won the National Outstanding Youth Science Fund, the Ministry of Education China University Natural Science Award two second prizes, Shanghai Science and Technology Progress Award two second prizes, excellent textbook first prize and two teaching achievement awards two prizes.
3 Fundamentals of Vibration Mechanics and MATLAB Application – Bao Wenbo – Tsinghua University Press
F4401001190309 TB123-39 / 1 2nd Floor Chinese Books 085 Row A Side 07 Frame 06 Floor
graduate level
Chapter 0 Introduction 0.1 Brief history of the development of vibration mechanics 0.2 Basic concepts of vibration mechanics 0.2.1 Basic physical quantities of vibration 0.2.2 Simple harmonic motion and its representation 0.2.3 Classification of vibration 0 .3 Basic methods for studying vibration problems 0.3.1 Research contents of vibration mechanics 0.3.2 Simplification and mechanical model of vibration system 0.3.3 Dynamic degrees of freedom of vibration system 0.3.4 Research on vibration mechanics Method 0.4 Engineering Application of Vibration Theory Chapter 1 Free Vibration of Single Degree of Freedom System 1.1 Simplification and Model of Vibration System 1.1.1 Elastic Element 1.1.2 Damping Element 1.1.3 Mass Element 1.1.4 Equivalent single-degree-of-freedom vibration system 1.2 Single-degree-of-freedom linear system vibration differential equation 1.2.1 Force-excited vibration differential equation 1.2.2 Basic excitation vibration differential equation 1.2.3 Static Effect of force on vibration differential equation 1.2.4 Linearization of vibration system 1.3 Free vibration of undamped system 1.3.1 Vibration solution of single-degree-of-freedom undamped system 1.3.2 Determination of natural frequency Method 1.3.3 Energy method 1.4 Free vibration with viscous damping system 1.5 MATL AB calculation example Chapter 2 Forced vibration of a single degree of freedom system 2.1 Forced vibration under harmonic excitation 2.1.1 Forced vibration of undamped system 2.1.2 Forced vibration of damped system 2.1.3 Complex solution method of forced vibration 2.1.4 Energy balance and Equivalent damping 2.2 Forced vibration when the foundation performs simple harmonic motion 2.2.1 Vibration equation 2.2.2 Steady-state vibration response 2.3 Isolation of vibration 2.3.1 Active vibration isolation 2.3.2 Passive vibration isolation 2.4 Forced vibration under periodic excitation 2.4.1 Superposition principle 2.4.2 Periodic excitation function and its Fourier expansion 2.4.3 Fourier series solution 2.5 Non-periodic excitation Forced vibration under 2.5.1 Impulse response method 2.5.2 Fourier integral method 2.6 MATLAB calculation example Chapter 3 Vibration of two-degree-of-freedom system 3.1 Differential equation of motion of two-degree-of-freedom vibration system 3 .2 Free vibration of undamped system 3.2.1 Equation of motion 3.2.2 Natural frequency and modes 3.2.3 Free vibration of undamped system 3.3 Coordinate coupling and principal coordinates 3.3.1 Coordinates Coupling 3.3.2 Physical coordinates and modal coordinates 3.4 Forced vibration under harmonic excitation 3.4.1 Forced vibration of undamped system 3.4.2 Viscous Solution of Forced Vibration of Damping System 3.4.3 Complex solution with viscous damping Method 3.5 Dynamic vibration reduction 3.6 Flapping vibration 3.7 Positive semidefinite system 3.8 Vibration characteristics of two-degree-of-freedom system 3.9 MATLAB example Chapter 4 Vibration of multi-degree-of-freedom system 4.1 Establishment of multi-degree-of-freedom system model 4.2 Establishment of equations of motion for multi-degree-of-freedom systems 4.2.1 Newton's second law 4.2.2 Lagrangian equation method 4.2.3 Influential coefficient method 4.2.4 Matrix of motion equations for multi-degree-of-freedom systems Representation method 4.3 Natural frequency and modal vector of multi-degree-of-freedom system 4.3.1 Eigenvalue problem 4.3.2 Natural frequency and modal vector 4.4 Modal analysis of multi-degree-of-freedom system 4.4 1 Orthogonality of modal vectors 4.4.2 Modal matrix 4.4.3 Modal coordinates 4.4.4 Regularized modes 4.4.5 Modal equations 4.5 Undamped multi-degree-of-freedom systems Vibration 4.5.1 Free vibration 4.5.2 Forced vibration 4.6 Modal analysis of general multi-degree-of-freedom systems 4.7 MATLAB examples Chapter 5 Vibration of continuous systems 5.1 Transverse vibration of strings 5 ．1.1 The vibration equation of the string 5.1.2 The solution of the free vibration equation of the string 5.4 The bending vibration of the beam 5.2 Longitudinal Vibration of Rod 5.3 Torsional vibration of rod 5.4.1 Equation of motion of beam bending vibration 5.4.2 Solution of free vibration of beam 5.4.3 Natural frequency and mode function 5.5 Shear deformation, rotational inertia and axis Effect of directional force 5.5.1 Effect of shear deformation and rotational inertia 5.5.2 Effect of axial force 5.6 Orthogonality of vibration mode function 5.7 Forced vibration of continuous system 5.7.1 Differential equations with damped motion 5.7.2 Generalized coordinate motion differential equations and their solutions 5.8 MATLAB examples 5.8.1 pdepe () function 5.8.2 pde toolbox toolbox 5.8.3 Examples Chapter 6 Approximate calculation method for vibration analysis