Dynamics and Vibration

Preface xi

Acknowledgements xiii

List of symbols xiv

Part I: Dynamics

1 Kinematics of Particles 3

1.1 Introduction 4

1.2 Rectilinear motion 8

1.3 Curvilinear motion 17

1.4 Tutorial sheet 36

2 Kinematics of Rigid Bodies 57

2.1 Introduction 58

2.2 Rigid body motion 58

2.3 Kinematics of wheels and gears 60

2.4 Kinematics of linkages and mechanisms 71

2.5 Tutorial sheet 95

3 Kinetics of Particles 113

3.1 Introduction 114

3.2 Newton’s laws 115

3.3 Force and acceleration 119

3.4 Work and energy 127

3.5 Impulse and momentum 136

3.6 Tutorial sheet 147

4 Kinetics of Rigid Bodies 167

4.1 Introduction 168

4.2 Force and acceleration 168

4.3 Work and energy 191

4.4 Impulse and momentum 201

4.5 Tutorial sheet 210

5 Balancing of Machines 229

5.1 Introduction 230

5.2 Balancing of rotating masses 230

5.3 Balancing of reciprocating engines 242

5.4 Tutorial sheet 253

Part II: Vibration

6 Free Vibration of Systems with a Single Degree of Freedom 265

6.1 Introduction 266

6.2 Undamped free vibration 268

6.3 Viscous damped free vibration 286

6.4 Tutorial sheet 300

7 Forced Vibration of Systems with a Single Degree of Freedom 315

7.1 Introduction 316

7.2 Undamped forced vibration – Harmonic force 317

7.3 Viscous damped forced vibration – harmonic force 324

7.4 General forced response 333

7.5 Vibration isolation 339

7.6 Tutorial sheet 350

8 Vibration of Systems with Two Degrees of Freedom 363

8.1 Introduction 364

8.2 Deriving the equations of motion 365

8.3 Undamped free vibration 371

8.4 Torsional vibration 385

8.5 Undamped forced vibrations 388

8.6 Vibration absorbers 394

8.7 Viscous damping 401

8.8 Tutorial sheet 405

9 Vibration of Continuous Systems 417

9.1 Introduction 418

9.2 Lateral vibration of a cable or string 418

9.3 Longitudinal vibration of a bar 428

9.4 Lateral vibration of a beam 438

9.5 Whirling shafts 448

9.6 Tutorial sheet 456

10 Finite-Element Method 467

10.1 Introduction 468

10.2 Bar element 468

10.3 Beam element 484

10.4 Guidelines for using Ansys 508

10.5 Tutorial sheet 510

Appendix A DAMA and Guidelines for Simulations 519

Appendix B Properties of Area 555

Appendix c Equivalent Stiffness for Combinations of Springs 557

Appendix d Summary of Formulas 561

Index 567