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Theory of Vibration with Applications - William Thomson

Theory of Vibration with Applications

Paperback

Published: 1st February 1996
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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 continous system theory to simplified models for the calculation of natural frequencies.

Preface
The SI System of Unitsp. 1
Oscillatory Motionp. 5
Harmonic Motionp. 6
Periodic Motionp. 9
Vibration Terminologyp. 12
Free Vibrationp. 17
Vibration Modelp. 17
Equations of Motion: Natural Frequencyp. 18
Energy Methodp. 22
Rayleigh Method: Effective Massp. 24
Principle of Virtual Workp. 26
Viscously Damped Free Vibrationp. 28
Logarithmic Decrementp. 33
Coulomb Dampingp. 35
Harmonically Excited Vibrationp. 51
Forced Harmonic Vibrationp. 51
Rotating Unbalancep. 56
Rotor Unbalancep. 58
Whirling of Rotating Shaftsp. 61
Support Motionp. 66
Vibration Isolationp. 68
Energy Dissipated by Dampingp. 70
Equivalent Viscous Dampingp. 73
Structural Dampingp. 75
Sharpness of Resonancep. 77
Vibration-Measuring Instrumentsp. 78
Transient Vibrationp. 92
Impulse Excitationp. 92
Arbitrary Excitationp. 94
Laplace Transform Formulationp. 97
Pulse Excitation and Rise Timep. 100
Shock Response Spectrump. 103
Shock Isolationp. 108
Finite Difference Numerical Computationp. 108
Runge-Kutta Method (Method 2)p. 117
Systems With Two Or More Degrees of Freedomp. 130
The Normal Mode Analysisp. 131
Initial Conditionsp. 135
Coordinate Couplingp. 138
Forced Harmonic Vibrationp. 143
Digital Computationp. 145
Vibration Absorberp. 150
Centrifugal Pendulum Vibration Absorberp. 152
Vibration Damperp. 154
Properties of Vibrating Systemsp. 171
Flexibility Influence Coefficientsp. 172
Reciprocity Theoremp. 175
Stiffness Influence Coefficientsp. 176
Stiffness Matrix of Beam Elementsp. 179
Static Condensation for Pinned Jointsp. 183
Orthogonality of Eigenvectorsp. 185
Modal Matrix Pp. 187
Decoupling Forced Vibration Equationsp. 189
Modal Damping in Forced Vibrationp. 190
Normal Mode Summationp. 192
Equal Rootsp. 195
Unrestrained (Degenerate) Systemsp. 197
Lagrange's Equationp. 207
Generalized Coordinatesp. 207
Virtual Workp. 212
Lagrange's Equationp. 215
Kinetic Energy, Potential Energy, and Generalized Force in Terms of Generalized Coordinates qp. 221
Assumed Mode Summationp. 223
Computational Methodsp. 234
Root Solvingp. 235
Gauss Eliminationp. 236
Matrix Iterationp. 238
Convergence of the Iteration Procedurep. 240
Convergence to Higher Modesp. 241
The Dynamic Matrixp. 246
Transformation of Coordinates (Standard Computer Form)p. 247
Systems with Discrete Mass Matrixp. 248
Cholesky Decompositionp. 249
Jacobi Diagonalizationp. 253
Computer Program Notesp. 260
Description of Computer Programsp. 261
Vibration of Continuous Systemsp. 268
Vibrating Stringp. 268
Longitudinal Vibration of Rodsp. 271
Torsional Vibration of Rodsp. 273
Vibration of Suspension Bridgesp. 276
Euler Equation for Beamsp. 281
Effect of Rotary Inertia and Shear Deformationp. 286
System with Repeated Identical Sectionsp. 289
Introduction to the Finite Element Methodp. 301
Element Stiffness and Massp. 301
Stiffness and Mass for the Beam Elementp. 306
Transformation of Coordinates (Global Coordinates)p. 309
Element Stiffness and Element Mass in Global Coordinatesp. 312
Vibrations Involving Beam Elementsp. 317
Spring Constraints on Structurep. 324
Generalized Force for Distributed Loadp. 327
Generalized Force Proportional to Displacementp. 328
Mode-Summation Procedures for Continuous Systemsp. 345
Mode-Summation Methodp. 345
Beam Orthogonality Including Rotary Inertia and Shear Deformationp. 351
Normal Modes of Constrained Structuresp. 353
Mode-Acceleration Methodp. 358
Component-Mode Synthesisp. 360
Classical Methodsp. 371
Rayleigh Methodp. 371
Dunkerley's Equationp. 379
Rayleigh-Ritz Methodp. 384
Holzer Methodp. 387
Digital Computer Program for the Torsional Systemp. 390
Myklestad's Method for Beamsp. 393
Coupled Flexure-Torsion Vibrationp. 397
Transfer Matricesp. 399
Systems with Dampingp. 400
Geared Systemp. 403
Branched Systemsp. 404
Transfer Matrices for Beamsp. 406
Random Vibrationsp. 419
Random Phenomenap. 419
"Time Averaging and Expected Valuep. 420
Frequency Response Functionp. 422
Probability Distributionp. 425
Correlationp. 431
Power Spectrum and Power Spectral Densityp. 435
Fourier Transformsp. 441
FTs and Responsep. 448
Nonlinear Vibrationsp. 461
Phase Planep. 462
Conservative Systemsp. 463
Stability of Equilibriump. 466
Method of Isoclinesp. 468
Perturbation Methodp. 470
Method of Iterationp. 473
Self-Excited Oscillationsp. 477
Runge-Kutta Methodp. 479
App. A: Specifications of Vibration Boundsp. 488
App. B: Introduction to Laplace Transformationp. 490
App. C: Determinants and Matricesp. 496
App. D: Normal Modes of Uniform Beamsp. 509
App. E: Lagrange's Equationp. 518
App. F: Computer Programsp. 521
Answers to Selected Problemsp. 527
Indexp. 541
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780748743803
ISBN-10: 0748743804
Audience: General
Format: Paperback
Language: English
Number Of Pages: 558
Published: 1st February 1996
Publisher: UCL PR
Country of Publication: GB
Dimensions (cm): 23.37 x 15.49  x 3.05
Weight (kg): 0.79
Edition Number: 4