Elements of Vibration Analysis

Elements of Vibration Analysis
اسم المؤلف
Leonard Meiroviteh
3 أغسطس 2019
(لا توجد تقييمات)

Elements of Vibration Analysis
Second Edition
Leonard Meiroviteh
College of Engineering
Virginia Polytechnic Institute and State University
Chapter 1 Free Response of Single-degree-of-freedom
Linear Systems
1.1 General Considerations
1.2 Characteristics of Discrete System Components
1.3 Differential Equations of Motion for First-order and Secondorder Linear Systems
1.4 Small Motions About Equilibrium Positions
1.5 Force-free Response of First-order Systems
1.6 Harmonic Oscillator
1.7 Free Vibration of Damped Second-order Systems
1.8 Logarithmic Decrement
1.9 Coulomb Damping. Dry Friction
Chapter 2 Forced Response of Single-degree-of-freedom
Linear Systems
2.1 General Considerations
2.2 Response of First-order Systems to Harmonic Excitation.
Frequency Response
2.3 Response of Second-order Systems to Harmonic Excitation
2.4 Rotating Unbalanced Masses
2.5 Whirling of Rotating Shafts
2.6 Harmonic Motion of the Support
2.7 Complex Vector Representation of Harmonic Motion
2.8 Vibration Isolation
2.9 Vibration Measuring Instruments
2.10 Energy Dissipation. Structural Damping
2.11 the Superposition Principle
2.12 Response to Periodic Excitation. Fourier Series
2.13 the Unit Impulse. Impulse Response
2.14 the Unit Step Function. Step Response
2.15 Response to Arbitrary Excitation. The Convolution Integral
2.16 Shock Spectrum
2.17 System Response by the Laplace Transformation Method.
Transfer Function
2.18 General System Response
Chapter 3 Two-degree-of-freedom Systems
3.1 Introduction
3.2 Equations of Motion for a Two-degree-of-freedom System
3.3 Free Vibration of Undamped Systems. Natural Modes
^3.5 3, Coordinate Orthogonality Transformations of Modes. Natural . Coupling Coordinates
3.6 Response of a Two-degree-of-freedom System to Initial
3.7 Beat Phenomenon
3.8 Response of a Two-degree-of-freedom System to Harmonic
3.9 Undamped Vibration Absorbers
Chapter 4 Multi-degree-of-freedom Systems
4.1 Introduction
4.2 Newton’s Equations of Motion. Generalized Coordinates
4.3 Equations of Motion for Linear Systems. Matrix Formulation
4.4 Influence Coefficients
4.5 Properties of the Stiffness and Inertia Coefficients
4.6 Linear Transformations. Coupling
L4j\ Undamped Free Vibration. Eigenvalue Problem
( 4.8 Orthogonality of Modal Vectors. Expansion Theorem
4.10 4^9 Solution Response of of Systems the Eigenvalue to Initialproblem Excitationby . Modal the Characteristic Analysis
4.11 Solution of the Eigenvalue Problem by the Matrix Iteration.
Power Method Using Matrix Deflation
4.12 Systems Admitting Rigid-body Motions
4.13 Rayleigh’s Quotient
4.14 General Response of Discrete Linear Systems. Modal Analysis
Chapter 5 Continuous Systems. Exact Solutions
5.1 General Discussion
5.2 Relation Between Discrete and Continuous Systems. Boundaryvalue Problem
5.3 Free Vibration. The Eigenvalue Problem
5.4 Continuous Versus Discrete Models for the Axial Vibration of
5.5 Bending Vibration of Bars. Boundary Conditions
5.6 Natural Modes of a Bar in Bending Vibration
5.7 Orthogonality of Natural Modes. Expansion Theorem
“(5jp. Rayleigh’s Quotient
5.9 Response of Systems by Modal Analysis
5.10 the Wave Equation
5.11 Kinetic and Potential Energy for Continuous Systems
Chapter 6 Elements of Analytical Dynamics
6.1 General Discussion
6.2 Work and Energy
6.3 the Principle of Virtual Work
6.4 D’alembert’s Principle
6.5 Lagrange’s Equations of Motion
6.6 Lagrange’s Equations of Motion for Linear Systems
Chapter 7 Continuous Systems. Approximate Methods
^ 7.1 7.2 General Rayleigh’considerations S Energy Method
7.3 the Rayleigh-ritz Method. The Inclusion Principle
7.4 Assumed-modes Method
7.5 Symmetric and Antisymmetric Modes
7.6 Response of Systems by the Assumed-modes Method
7.7 Holzer’s Method for Torsional Vibration
7.8 Lumped-parameter Method Employing Influence Coefficients,
. Chapter 8 the Finite Element Method
8.1 General Considerations
8.2\ Derivation of the Element Stiffness Matrix by the Direct
8.3 Element Equations of Motion. A Consistent Approach
8.4 Reference Systems
8.5 the Equations of Motion for the Complete System. The
Assembling Process
8.6 the Eigenvalue Problem. The Finite Element Method as a
Rayleigh-ritz Method
8.7 Higher-degree Interpolation Functions. Internal Nodes
8.8 the Hierarchical Finite Element Method
8.9 the Inclusion Principle Revisited
Nonlinear Systems. Geometric Theory
Fundamental Concepts in Stability
Single-degree-of-freedom Autonomous Systems. Phase Plane
Routh-hurwitz Criterion
Conservative Systems. Motion in the Large
Limit Cycles
Liapunov’s Direct Method
Chapter 9
Nonlinear Systems. Perturbation Methods
General Considerations
The Fundamental Perturbation Technique
Secular Terms
Lindstedt’s Method
Forced Oscillation of Quasi-harmonic Systems. Jump
Subharmonics and Combination Harmonics
Systems With Time-dependent Coefficients. Mathieu’s Equation
Random Vibrations
General Considerations
Ensemble Averages. Stationary Random Processes
Time Averages. Ergodic Random Processes
Mean Square Values
Probability Density Functions
Description of Random Data in Terms of Probability Density
Properties of Autocorrelation Functions
Response to Random Excitation. Fourier Transforms
Power Spectral Density Functions
Narrowband and Wideband Random Processes
Response of Linear Systems to Stationary Random Excitation
Response of Single-degree-of-freedom Systems to Random
Joint Probability Distribution of Two Random Variables
Joint Properties of Stationary Random Processes
Joint Properties of Ergodic Random Processes
Response Cross-correlation Functions for Linear Systems
Response of Multi-degree-of-freedom Systems to Random
Response of Continuous Systems to Random Excitation
Chapter 11
Contents Xlil
Chapter 12 Computational Techniques
12.2 Response of Linear Systems by the Transition Matrix
12.3 Computation of the Transition Matrix
Alternative Computation of the Transition Matrix
112.5 ], Response of General Damped Systems by the Transition
12.6 Discrete-time Systems
12.7 the Runge-kutta Methods
12.8 the Frequency-domain Convolution Theorem
12.9 Fourier Series as a Special Case of the Fourier Integral
12.10 Sampled Functions
12.11 the Discrete Fourier Transform
12.12 the Fast Fourier Transform
Appendixes 519
A Fourier Series
Orthogonal Sets of Functions
Trigonometric Series
Complex Form of Fourier Series
B Elements of Laplace Transformation
General Definitions
Transformation of Derivatives
Transformation of Ordinary Differential Equations
The Inverse Laplace Transformation
The Convolution Integral. Borel’s Theorem
Table of Laplace Transform Pairs
C Elements of Linear Algebra
General Considerations
Vector Spaces
Linear Transformations
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