Theory of Vibrations With Applications

by Thomson, William T.; Dahleh, Marie Dillon

• ISBN13: 9780136510680
• ISBN10: 013651068X
• Edition: 5th
• Format: Hardcover
• Copyright: 1997-08-07
• Publisher: Pearson

Summary

A thorough treatment of vibration theory and its engineering applications, from simple degree to multi degree-of-freedom system.Focuses on the physical aspects of the mathematical concepts necessary to describe the vibration phenomena. Provides many example applications to typical problems faced by practicing engineers. Includes a chapter on computer methods, and an accompanying disk with four basic Fortran programs covering most of the calculations encountered in vibration problems.

Table of Contents

PREFACE	xi
THE SI SYSTEM OF UNITS	1	(4)
CHAPTER 1 OSCILLATORY MOTION	5	(11)
1.1 Harmonic Motion	6	(3)
1.2 Periodic Motion	9	(2)
1.3 Vibration Terminology	11	(5)
CHAPTER 2 FREE VIBRATION	16	(33)
2.1 Vibration Model	16	(1)
2.2 Equation of Motion: Natural Frequency	16	(4)
2.3 Energy Method	20	(3)
2.4 Rayleigh Method: Effective Mass	23	(2)
2.5 Principle of Virtual Work	25	(2)
2.6 Viscously Damped Free Vibration	27	(4)
2.7 Logarithmic Decrement	31	(4)
2.8 Coulomb Damping	35	(14)
CHAPTER 3 HARMONICALLY EXCITED VIBRATION	49	(40)
3.1 Forced Harmonic Vibration	49	(4)
3.2 Rotating Unbalance	53	(3)
3.3 Rotor Unbalance	56	(3)
3.4 Whirling of Rotating Shafts	59	(4)
3.5 Support Motion	63	(2)
3.6 Vibration Isolation	65	(2)
3.7 Energy Dissipated by Damping	67	(3)
3.8 Equivalent Viscous Damping	70	(2)
3.9 Structural Damping	72	(2)
3.10 Sharpness of Resonance	74	(1)
3.11 Vibration-Measuring Instruments	75	(14)
CHAPTER 4 TRANSIENT VIBRATION	89	(37)
4.1 Impulse Excitation	89	(2)
4.2 Arbitrary Excitation	91	(3)
4.3 Laplace Transform Formulation	94	(3)
4.4 Pulse Excitation and Rise Time	97	(3)
4.5 Shock Response Spectrum	100	(4)
4.6 Shock Isolation	104	(1)
4.7 Finite Difference Numerical Computation	105	(7)
4.8 Runge-Kutta Method	112	(14)
CHAPTER 5 SYSTEMS WITH TWO OR MORE DEGREES OF FREEDOM	126	(37)
5.1 The Normal Mode Analysis	127	(4)
5.2 Initial Conditions	131	(3)
5.3 Coordinate Coupling	134	(5)
5.4 Forced Harmonic Vibration	139	(2)
5.5 Finite Difference Method for Systems of Equations	141	(3)
5.6 Vibration Absorber	144	(1)
5.7 Centrifugal Pendulum Vibration Absorber	145	(2)
5.8 Vibration Damper	147	(16)
CHAPTER 6 PROPERTIES OF VIBRATING SYSTEMS	163	(36)
6.1 Flexibility Influence Coefficients	164	(3)
6.2 Reciprocity Theorem	167	(5)
6.3 Stiffness Influence Coefficients	172	(4)
6.4 Stiffness Matrix of Beam Elements	176	(1)
6.5 Static Condensation for Pinned Joints	176	(1)
6.6 Orthogonality of Eigenvectors	177	(2)
6.7 Modal Matrix	179	(2)
6.8 Decoupling Forced Vibration Equations	181	(1)
6.9 Modal Damping in Forced Vibration	182	(1)
6.10 Normal Mode Summation	183	(4)
6.11 Equal Roots	187	(2)
6.12 Unrestrained (Degenerate) Systems	189	(10)
CHAPTER 7 LAGRANGE'S EQUATION	199	(28)
7.1 Generalized Coordinates	199	(5)
7.2 Virtual Work	204	(3)
7.3 Lagrange's Equation	207	(7)
7.4 Kinetic Energy, Potential Energy, and Generalized Force in Terms of Generalized Coordinates q	214	(2)
7.5 Assumed Mode Summation	216	(11)
CHAPTER 8 COMPUTATIONAL METHODS	227	(41)
8.1 Root Solving	227	(2)
8.2 Eigenvectors by Gauss Elimination	229	(1)
8.3 Matrix Iteration	230	(3)
8.4 Convergence of the Iteration Procedure	233	(1)
8.5 The Dynamic Matrix	233	(1)
8.6 Transformation Coordinates (Standard Computer Form)	234	(1)
8.7 Systems with Discrete Mass Matrix	235	(2)
8.8 Cholesky Decomposition	237	(5)
8.9 Jacobi Diagonalization	242	(5)
8.10 QR Method for Eigenvalue and Eigenvector Calculation	247	(21)
CHAPTER 9 VIBRATION OF CONTINUOUS SYSTEMS	268	(19)
9.1 Vibrating String	268	(3)
9.2 Longitudinal Vibration of Rods	271	(2)
9.3 Torsional Vibration of Rods	273	(3)
9.4 Vibration of Suspension Bridges	276	(5)
9.5 Euler Equation for Beams	281	(8)
9.6 System with Repeated Identical Sections	289
CHAPTER 10 INTRODUCTION TO THE FINITE ELEMENT METHOD	287	(42)
10.1 Element Stiffness and Mass	287	(5)
10.2 Stiffness and Mass for the Beam Element	292	(3)
10.3 Transformation of Coordinates (Global Coordinates)	295	(2)
10.4 Element Stiffness and Element Mass in Global Coordinates	297	(5)
10.5 Vibrations Involving Beam Elements	302	(7)
10.6 Spring Constraints on Structure	309	(2)
10.7 Generalized Force for Distributed Load	311	(2)
10.8 Generalized Force Proportional to Displacement	313	(16)
CHAPTER 11 MODE-SUMMATION PROCEDURES FOR CONTINUOUS SYSTEMS	329	(22)
11.1 Mode-Summation Method	329	(6)
11.2 Normal Modes of Constrained Structures	335	(4)
11.3 Mode-Acceleration Method	339	(2)
11.4 Component-Mode Synthesis	341	(10)
CHAPTER 12 CLASSICAL METHODS	351	(44)
12.1 Rayleigh Method	351	(7)
12.2 Dunkerley's Equation	358	(5)
12.3 Rayleigh-Ritz Method	363	(3)
12.4 Holzer Method	366	(3)
12.5 Digital Computer Program for the Torsional System	369	(2)
12.6 Myklestad's Method for Beams	371	(4)
12.7 Coupled Flexure-Torsion Vibration	375	(1)
12.8 Transfer Matrices	376	(2)
12.9 Systems with Damping	378	(2)
12.10 Geared System	380	(1)
12.11 Branched Systems	381	(2)
12.12 Transfer Matrices for Beams	383	(12)
CHAPTER 13 RANDOM VIBRATIONS	395	(41)
13.1 Random Phenomena	395	(1)
13.2 Time Averaging and Expected Value	396	(2)
13.3 Frequency Response Function	398	(3)
13.4 Probability Distribution	401	(6)
13.5 Correlation	407	(4)
13.6 Power Spectrum and Power Spectral Density	411	(6)
13.7 Fourier Transforms	417	(7)
13.8 FTs and Response	424	(12)
CHAPTER 14 NONLINEAR VIBRATIONS	436	(26)
14.1 Phase Plane	436	(2)
14.2 Conservative Systems	438	(3)
14.3 Stability of Equilibrium	441	(2)
14.4 Method of Isoclines	443	(2)
14.5 Perturbation Method	445	(3)
14.6 Method of Iteration	448	(3)
14.7 Self-Excited Oscillations	451	(2)
14.8 Runge-Kutta Method	453	(9)
APPENDICES	462	(44)
A Specifications of Vibration Bounds	462	(2)
B Introduction to Laplace Transformation	464	(5)
C Determinants and Matirces	469	(10)
D Normal Modes of Uniform Beams	479	(8)
E Introduction to MATLAB(R)	487	(5)
F Computer Programs	492	(9)
G Convergence to Higher Modes	501	(5)
ANSWERS TO SELECTED PROBLEMS	506	(13)
INDEX	519