9780136510680

Theory of Vibrations With Applications

by ;
  • ISBN13:

    9780136510680

  • ISBN10:

    013651068X

  • Edition: 5th
  • Format: Hardcover
  • Copyright: 8/7/1997
  • Publisher: Pearson

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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

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