THEORY OF VIBRATION WITH APPLICATIONS FIFTH EDITIONpdf电子书版本下载

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THE SI SYSTEM OF UNITS 1

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 OR 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 285

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 462

A Specifications of Vibration Bounds 462

B Introduction to Laplace Transformation 464

C Determinants and Matirces 469

D Normal Modes of Uniform Beams 479

E Introduction to MATLAB？ 487

F Computer Programs 492

G Convergence to Higher Modes 501

ANSWERS TO SELECTED PROBLEMS 506

INDEX 519