Theory of Vibration With Applications/Book and Disk

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ISBN: 9780139153235 | 0139153233
Cover: Hardcover
Copyright: 10/1/1992

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This fourth edition of this volume 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. It adds coverage of the methods of assumed modes and incorporates a new section on suspension bridges to illustrate the application of the continuos system theory to simplified models for the calculation of natural frequencies.

Preface
The SI System of Units	p. 1
Oscillatory Motion	p. 5
Harmonic Motion	p. 6
Periodic Motion	p. 9
Vibration Terminology	p. 12
Free Vibration	p. 17
Vibration Model	p. 17
Equations of Motion: Natural Frequency	p. 18
Energy Method	p. 22
Rayleigh Method: Effective Mass	p. 24
Principle of Virtual Work	p. 26
Viscously Damped Free Vibration	p. 28
Logarithmic Decrement	p. 33
Coulomb Damping	p. 35
Harmonically Excited Vibration	p. 51
Forced Harmonic Vibration	p. 51
Rotating Unbalance	p. 56
Rotor Unbalance	p. 58
Whirling of Rotating Shafts	p. 61
Support Motion	p. 66
Vibration Isolation	p. 68
Energy Dissipated by Damping	p. 70
Equivalent Viscous Damping	p. 73
Structural Damping	p. 75
Sharpness of Resonance	p. 77
Vibration-Measuring Instruments	p. 78
Transient Vibration	p. 92
Impulse Excitation	p. 92
Arbitrary Excitation	p. 94
Laplace Transform Formulation	p. 97
Pulse Excitation and Rise Time	p. 100
Shock Response Spectrum	p. 103
Shock Isolation	p. 108
Finite Difference Numerical Computation	p. 108
Runge-Kutta Method (Method 2)	p. 117
Systems With Two Or More Degrees of Freedom	p. 130
The Normal Mode Analysis	p. 131
Initial Conditions	p. 135
Coordinate Coupling	p. 138
Forced Harmonic Vibration	p. 143
Digital Computation	p. 145
Vibration Absorber	p. 150
Centrifugal Pendulum Vibration Absorber	p. 152
Vibration Damper	p. 154
Properties of Vibrating Systems	p. 171
Flexibility Influence Coefficients	p. 172
Reciprocity Theorem	p. 175
Stiffness Influence Coefficients	p. 176
Stiffness Matrix of Beam Elements	p. 179
Static Condensation for Pinned Joints	p. 183
Orthogonality of Eigenvectors	p. 185
Modal Matrix P	p. 187
Decoupling Forced Vibration Equations	p. 189
Modal Damping in Forced Vibration	p. 190
Normal Mode Summation	p. 192
Equal Roots	p. 195
Unrestrained (Degenerate) Systems	p. 197
Lagrange's Equation	p. 207
Generalized Coordinates	p. 207
Virtual Work	p. 212
Lagrange's Equation	p. 215
Kinetic Energy, Potential Energy, and Generalized Force in Terms of Generalized Coordinates q	p. 221
Assumed Mode Summation	p. 223
Computational Methods	p. 234
Root Solving	p. 235
Gauss Elimination	p. 236
Matrix Iteration	p. 238
Convergence of the Iteration Procedure	p. 240
Convergence to Higher Modes	p. 241
The Dynamic Matrix	p. 246
Transformation of Coordinates (Standard Computer Form)	p. 247
Systems with Discrete Mass Matrix	p. 248
Cholesky Decomposition	p. 249
Jacobi Diagonalization	p. 253
Computer Program Notes	p. 260
Description of Computer Programs	p. 261
Vibration of Continuous Systems	p. 268
Vibrating String	p. 268
Longitudinal Vibration of Rods	p. 271
Torsional Vibration of Rods	p. 273
Vibration of Suspension Bridges	p. 276
Euler Equation for Beams	p. 281
Effect of Rotary Inertia and Shear Deformation	p. 286
System with Repeated Identical Sections	p. 289
Introduction to the Finite Element Method	p. 301
Element Stiffness and Mass	p. 301
Stiffness and Mass for the Beam Element	p. 306
Transformation of Coordinates (Global Coordinates)	p. 309
Element Stiffness and Element Mass in Global Coordinates	p. 312
Vibrations Involving Beam Elements	p. 317
Spring Constraints on Structure	p. 324
Generalized Force for Distributed Load	p. 327
Generalized Force Proportional to Displacement	p. 328
Mode-Summation Procedures for Continuous Systems	p. 345
Mode-Summation Method	p. 345
Beam Orthogonality Including Rotary Inertia and Shear Deformation	p. 351
Normal Modes of Constrained Structures	p. 353
Mode-Acceleration Method	p. 358
Component-Mode Synthesis	p. 360
Classical Methods	p. 371
Rayleigh Method	p. 371
Dunkerley's Equation	p. 379
Rayleigh-Ritz Method	p. 384
Holzer Method	p. 387
Digital Computer Program for the Torsional System	p. 390
Myklestad's Method for Beams	p. 393
Coupled Flexure-Torsion Vibration	p. 397
Transfer Matrices	p. 399
Systems with Damping	p. 400
Geared System	p. 403
Branched Systems	p. 404
Transfer Matrices for Beams	p. 406
Random Vibrations	p. 419
Random Phenomena	p. 419
"Time Averaging and Expected Value	p. 420
Frequency Response Function	p. 422
Probability Distribution	p. 425
Correlation	p. 431
Power Spectrum and Power Spectral Density	p. 435
Fourier Transforms	p. 441
FTs and Response	p. 448
Nonlinear Vibrations	p. 461
Phase Plane	p. 462
Conservative Systems	p. 463
Stability of Equilibrium	p. 466
Method of Isoclines	p. 468
Perturbation Method	p. 470
Method of Iteration	p. 473
Self-Excited Oscillations	p. 477
Runge-Kutta Method	p. 479
App. A: Specifications of Vibration Bounds	p. 488
App. B: Introduction to Laplace Transformation	p. 490
App. C: Determinants and Matrices	p. 496
App. D: Normal Modes of Uniform Beams	p. 509
App. E: Lagrange's Equation	p. 518
App. F: Computer Programs	p. 521
Answers to Selected Problems	p. 527
Index	p. 541
Table of Contents provided by Blackwell. All Rights Reserved.

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Theory of Vibration With Applications/Book and Disk

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