Theory Of Vibration With Applications / Edition 4

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More About This Textbook

Overview

This edition features a new chapter on computational methods that presents the basic principles on which most modern computer programs are developed. It introduces an example on rotor balancing and expands on the section on shock spectrum and isolation.

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Product Details

  • ISBN-13: 9780748743803
  • Publisher: CRC Press
  • Publication date: 2/1/1996
  • Edition number: 4
  • Pages: 560
  • Product dimensions: 6.14 (w) x 9.21 (h) x 1.14 (d)

Table of Contents

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Preface
The SI System of Units 1
1 Oscillatory Motion 5
1.1 Harmonic Motion 6
1.2 Periodic Motion 9
1.3 Vibration Terminology 12
2 Free Vibration 17
2.1 Vibration Model 17
2.2 Equations of Motion: Natural Frequency 18
2.3 Energy Method 22
2.4 Rayleigh Method: Effective Mass 24
2.5 Principle of Virtual Work 26
2.6 Viscously Damped Free Vibration 28
2.7 Logarithmic Decrement 33
2.8 Coulomb Damping 35
3 Harmonically Excited Vibration 51
3.1 Forced Harmonic Vibration 51
3.2 Rotating Unbalance 56
3.3 Rotor Unbalance 58
3.4 Whirling of Rotating Shafts 61
3.5 Support Motion 66
3.6 Vibration Isolation 68
3.7 Energy Dissipated by Damping 70
3.8 Equivalent Viscous Damping 73
3.9 Structural Damping 75
3.10 Sharpness of Resonance 77
3.11 Vibration-Measuring Instruments 78
4 Transient Vibration 92
4.1 Impulse Excitation 92
4.2 Arbitrary Excitation 94
4.3 Laplace Transform Formulation 97
4.4 Pulse Excitation and Rise Time 100
4.5 Shock Response Spectrum 103
4.6 Shock Isolation 108
4.7 Finite Difference Numerical Computation 108
4.8 Runge-Kutta Method (Method 2) 117
5 Systems With Two Or More Degrees of Freedom 130
5.1 The Normal Mode Analysis 131
5.2 Initial Conditions 135
5.3 Coordinate Coupling 138
5.4 Forced Harmonic Vibration 143
5.5 Digital Computation 145
5.6 Vibration Absorber 150
5.7 Centrifugal Pendulum Vibration Absorber 152
5.8 Vibration Damper 154
6 Properties of Vibrating Systems 171
6.1 Flexibility Influence Coefficients 172
6.2 Reciprocity Theorem 175
6.3 Stiffness Influence Coefficients 176
6.4 Stiffness Matrix of Beam Elements 179
6.5 Static Condensation for Pinned Joints 183
6.6 Orthogonality of Eigenvectors 185
6.7 Modal Matrix P 187
6.8 Decoupling Forced Vibration Equations 189
6.9 Modal Damping in Forced Vibration 190
6.10 Normal Mode Summation 192
6.11 Equal Roots 195
6.12 Unrestrained (Degenerate) Systems 197
7 Lagrange's Equation 207
7.1 Generalized Coordinates 207
7.2 Virtual Work 212
7.3 Lagrange's Equation 215
7.4 Kinetic Energy, Potential Energy, and Generalized Force in Terms of Generalized Coordinates q 221
7.5 Assumed Mode Summation 223
8 Computational Methods 234
8.1 Root Solving 235
8.2 Gauss Elimination 236
8.3 Matrix Iteration 238
8.4 Convergence of the Iteration Procedure 240
8.5 Convergence to Higher Modes 241
8.6 The Dynamic Matrix 246
8.7 Transformation of Coordinates (Standard Computer Form) 247
8.8 Systems with Discrete Mass Matrix 248
8.9 Cholesky Decomposition 249
8.10 Jacobi Diagonalization 253
8.11 Computer Program Notes 260
8.12 Description of Computer Programs 261
9 Vibration of Continuous Systems 268
9.1 Vibrating String 268
9.2 Longitudinal Vibration of Rods 271
9.3 Torsional Vibration of Rods 273
9.4 Vibration of Suspension Bridges 276
9.5 Euler Equation for Beams 281
9.6 Effect of Rotary Inertia and Shear Deformation 286
9.7 System with Repeated Identical Sections 289
10 Introduction to the Finite Element Method 301
10.1 Element Stiffness and Mass 301
10.2 Stiffness and Mass for the Beam Element 306
10.3 Transformation of Coordinates (Global Coordinates) 309
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