Theory of vibration with applications / William T. Thomson, Marie Dillon Dahleh.

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