Theory of Vibrations With Applications

, by Thomson, William T.; Dahleh, Marie Dillon

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ISBN: 9780136510680 | 013651068X
Cover: Hardcover
Copyright: 8/7/1997

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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.

PREFACE

THE SI SYSTEM OF UNITS

(4)

CHAPTER 1 OSCILLATORY MOTION

(11)

1.1 Harmonic Motion

(3)

1.2 Periodic Motion

(2)

1.3 Vibration Terminology

(5)

CHAPTER 2 FREE VIBRATION

(33)

2.1 Vibration Model

(1)

2.2 Equation of Motion: Natural Frequency

(4)

2.3 Energy Method

(3)

2.4 Rayleigh Method: Effective Mass

(2)

2.5 Principle of Virtual Work

(2)

2.6 Viscously Damped Free Vibration

(4)

2.7 Logarithmic Decrement

(4)

2.8 Coulomb Damping

(14)

CHAPTER 3 HARMONICALLY EXCITED VIBRATION

(40)

3.1 Forced Harmonic Vibration

(4)

3.2 Rotating Unbalance

(3)

3.3 Rotor Unbalance

(3)

3.4 Whirling of Rotating Shafts

(4)

3.5 Support Motion

(2)

3.6 Vibration Isolation

(2)

3.7 Energy Dissipated by Damping

(3)

3.8 Equivalent Viscous Damping

(2)

3.9 Structural Damping

(2)

3.10 Sharpness of Resonance

(1)

3.11 Vibration-Measuring Instruments

(14)

CHAPTER 4 TRANSIENT VIBRATION

(37)

4.1 Impulse Excitation

(2)

4.2 Arbitrary Excitation

(3)

4.3 Laplace Transform Formulation

(3)

4.4 Pulse Excitation and Rise Time

(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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Theory of Vibrations With Applications

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