THEORY OF VIBRATION WITH APPLICATIONS【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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1 OSCILLATORY MOTION1

1.1 Introduction1

1.2 Harmonic Motion2

1.3 Harmonic Analysis5

1.4 Transient Time Function7

1.5 Random Time Function8

1.6 Properties of Oscillatory Motion9

2 FREE VIBRATION14

2.1 Force Summation Method14

2.2 The Energy Method17

2.3 Effective Mass19

2.4 Damped Free Vibration21

2.5 Logarithmic Decrement27

2.6 Coulomb Damping31

2.7 Stiffness and Flexibility32

3 HARMONICALLY EXCITED MOTION45

3.1 Introduction45

3.2 Forced Harmonic Vibration45

3.3 Rotating Unbalance49

3.4 Whirling of Rotating Shafts54

3.5 Support Motion56

3.6 Vibration Measuring Instruments58

3.7 Vibration Isolation62

3.8 Damping65

3.9 Equivalent Viscous Damping69

3.10 Structural Damping71

3.11 Sharpness of Resonance72

4 TRANSIENT VIBRATION79

4.1 Introduction79

4.2 Impulse Excitation79

4.3 Arbitrary Excitation81

4.4 The Laplace Transform Formulation88

4.5 Response Spectrum93

4.6 The Analog Computer98

4.7 Finite Difference Digital Computation108

4.8 The Runge-Kutta Computation117

5 TWO DEGREES OF FREEDOM SYSTEMS127

5.1 Introduction127

5.2 Normal Mode Vibration128

5.3 Coordinate Coupling134

5.4 Forced Harmonic Vibration138

5.5 Vibration Absorber141

5.6 The Centrifugal Pendulum Absorber142

5.7 The Vibration Damper144

5.8 Gyroscopic Effect on Rotating Shafts149

5.9 Digital Computation151

6 MULTIDEGREE OF FREEDOM SYSTEM166

6.1 Introduction166

6.2 The Flexibility and Stiffness Matrix167

6.3 Reciprocity Theorem170

6.4 Eigenvalues and Eigenvectors170

6.5 Orthogonal Properties of the Eigenvectors174

6.6 Repeated Roots175

6.7 The Modal Matrix P178

6.8 Forced Vibration and Coordinate Decoupling180

6.9 Forced Normal Modes of Damped Systems181

6.10 State Space Method186

7 LUMPED PARAMETER SYSTEMS196

7.1 Introduction196

7.2 Characteristic Equation197

7.3 Method of Influence Coeffcients197

7.4 Rayleigh Principle200

7.5 Dunkerley’s Formula209

7.6 Method of Matrix Iteration213

7.7 Calculation of Higher Modes215

7.8 Transfer Matrices （Holzer-Type Problems）219

7.9 Torsional System221

7.10 Geared System231

7.11 Branched Systems232

7.12 Beams234

7.13 Repeated Structures and Transfer Matrix242

7.14 Difference Equation245

8 CONTINUOUS SYSTEMS261

8.1 Introduction261

8.2 The Vibrating String262

8.3 Longitudinal Vibration of Rods265

8.4 Torsional Vibration of Rods267

8.5 The Euler Equation for the Beam271

8.6 Effect of Rotary Inertia and Shear Deformation275

8.7 Vibration of Membranes276

8.8 Digital Computation278

8.9 Transient Solution by Laplace Transforms286

9 LAGRANGE’S EQUATION295

9.1 Introduction295

9.2 Generalized Coordinates295

9.3 Principle of Virtual Work296

9.4 Development of Lagrange’s Equation300

9.5 Generalized Stiffness and Mass303

9.6 Mode Summation Method305

9.7 Beam Orthogonality，Including Rotary Inertia and Shear Deformation311

9.8 Normal Modes of Constrained Structures313

9.9 Mode-Acceleration Method318

9.10 Component Mode Synthesis320

10 RANDOM VIBRATION332

10.1 Introduction332

10.2 The Frequency Response Function334

10.3 Spectral Density336

10.4 Probability Distribution343

10.5 Correlation352

10.6 Fourier Transform355

10.7 Response of Continuous Structures to Random Excitation361

11 NONLINEAR VIBRATIONS370

11.1 Introduction370

11.2 The Phase Plane371

11.3 Conservative Systems373

11.4 Stability of Equilibrium375

11.5 Method of Isoclines378

11.6 The Delta Method380

11.7 Lienard’s Method383

11.8 Slopeline Numerical Integration385

11.9 The Perturbation Method389

11.10 Method of Iteration392

11.11 Self-Excited Oscillations397

11.12 Analog Computer Circuits for Nonlinear Systems399

11.13 The Runge-Kutta Method401

APPENDICES412

ANSWERS TO SELECTED PROBLEMS448

INDEX461