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1 INTRODUCTION 1

1.1 Introduction to Free Vibration 2

1.2 Harmonic Motion 8

1.3 Viscous Damping 14

1.4 Modeling and Energy Methods 23

1.5 Stiffness 34

1.6 Measurement 43

1.7 Design Considerations 48

1.8 Stability 53

1.9 Numerical Simulation of the Time Response 56

1.10 Coulomb Friction and the Pendulum 65

Problems 77

MATLAB Engineering Vibration Toolbox 87

Toolbox Problems 88

2 RESPONSE TO HARMONIC EXCITATION 89

2.1 Harmonic Excitation of Undamped Systems 90

2.2 Harmonic Excitation of Damped Systems 97

2.3 Alternative Representations 106

2.4 Base Excitation 112

2.5 Rotating Unbalance 120

2.6 Measurement 125

2.7 Other Forms of Damping 129

2.8 Numerical Simulation and Design 139

2.9 Nonlinear Response Properties 147

Problems 156

MATLAB Engineering Vibration Toolbox 167

Toolbox Problems 167

3 GENERAL FORCED RESPONSE 168

3.1 Impulse Response Function 170

3.2 Response to an Arbitrary Input 177

3.3 Response to an Arbitrary Periodic Input 183

3.4 Transform Methods 190

3.5 Response to Random Inputs 194

3.6 Shock Spectrum 202

3.7 Measurement via Transfer Functions 206

3.8 Stability 209

3.9 Numerical Simulation of the Response 213

3.10 Nonlinear Response Properties 224

Problems 232

MATLAB Engineering Vibration Toolbox 242

Toolbox Problems 242

4 MULTIPLE-DEGREE-OF-FREEDOM SYSTEMS 243

4.1 Two-Degree-of-Freedom Model （Undamped） 244

4.2 Eigenvalues and Natural Frequencies 255

4.3 Modal Analysis 267

4.4 More Than Two Degrees of Freedom 275

4.5 Systems with Viscous Damping 289

4.6 Modal Analysis of the Forced Response 294

4.7 Lagrange’s Equations 300

4.8 Examples 307

4.9 Computational Eigenvalue Problems of Vibration 319

4.10 Numerical Simulation of the Time Response 337

Problems 345

MATLAB Engineering Vibration Toolbox 357

Toolbox Problems 357

5 DESIGN FOR VIBRATION SUPPRESSION 359

5.1 Acceptable Levels of Vibration 360

5.2 Vibration Isolation 366

5.3 Vibration Absorbers 377

5.4 Damping in Vibration Absorption 384

5.5 Optimization 391

5.6 Viscoelastic Damping Treatments 399

5.7 Critical Speeds of Rotating Disks 404

5.8 Active Vibration Suppression 410

5.9 Practical Isolation Design 412

Problems 420

MATLAB Engineering Vibration Toolbox 430

Toolbox Problems 430

6 DISTRIBUTED-PARAMETER SYSTEMS 431

6.1 Vibration of a String or Cable 433

6.2 Modes and Natural Frequencies 436

6.3 Vibration of Rods and Bars 446

6.4 Torsional Vibration 452

6.5 Bending Vibration of a Beam 458

6.6 Vibration of Membranes and Plates 470

6.7 Models of Damping 475

6.8 Modal Analysis and the Forced Response 480

Problems 487

MATLAB Engineering Vibration Toolbox 493

Toolbox Problems 493

7 VIBRATION TESTING AND EXPERIMENTAL MODAL ANALYSIS 495

7.1 Measurement Hardware 497

7.2 Digital Signal Processing 501

7.3 Random Signal Analysis in Testing 506

7.4 Modal Data Extraction 509

7.5 Model Parameter by Circle Fitting 513

7.6 Mode Shape Measurement 517

7.7 Vibration Testing for Endurance and Diagnostics 523

7.8 Operational Deflection Shape Measurement 526

Problems 528

MATLAB Engineering Vibration Toolbox 532

Toolbox Problems 532

8 FINITE ELEMENT METHOD 533

8.1 Example：The Bar 535

8.2 Three-Element Bar 541

8.3 Beam Elements 546

8.4 Lumped Mass Matrices 553

8.5 Trusses 556

8.6 Model Reduction 560

Problems 563

MATLAB Engineering Vibration Toolbox 570

Toolbox Problems 570

APPENDIX A COMPLEX NUMBERS AND FUNCTIONS 571

APPENDIX B LAPLACE TRANSFORMS 577

APPENDIX C MATRIX BASICS 582

APPENDIX D THE VIBRATION LITERATURE 594

APPENDIX E LIST OF SYMBOLS 595

APPENDIX F INTRODUCTION TO MATLAB，MATHCAD AND MATHEMATICA 600

APPENDIX G ENGINEERING VIBRATION TOOLBOX AND WEB SUPPORT 601

REFERENCES 603

ANSWERS TO SELECTED PROBLEMS 605

INDEX 611