This book presents a new teaching methodology in Dynamics using E-learning, simulations and animation of mechanisms and mechanical vibrating systems. It covers Dynamics and Vibration modules that are taught at different undergraduate levels to the engineering students at Universities in the UK and worldwide.

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

Dynamics and Vibration: An Introduction is a textbook to support Dynamics and Vibration modules across a wide range of undergraduate engineering courses from first year to final year including civil, mechanical, aerospace and medical engineering. The unique DAMA software, included as a free online resource, generates computer simulations that provide students with a new way to visualise the motion of mechanisms and vibrating systems. By varying the input and output parameters of the simulations themselves, students can clearly see and understand the effects of system changes. Dynamics and Vibration: An Introduction is well structured and easy to understand, with a wealth of examples and tutorial questions. It offers lecutres and student of Dynamics and Vibration a practical and concise resource specifically for their needs. Topics covered include: motion of particles and rigid bodies with and without reference to masses and forces (Kinematics and Kinetics) including motion of wheels, gears, linkages and mechanisms; balancing of machines including rotating masses and multi-cylinder engines; free and forced vibration of a single degree of freedom (mass, a spring and a damper) including damped, damped systems and vibration isolators; free and forced vibration of two-degree of freedom systems including vibration of bars and lateral vibration absorbers; vibration of continuous systems including lateral vibration of cables, longitudinal vibration of bars and lateral vibration of beams using analytical solution and Finite Element Method.