Livija Cveticanin is Professor of the University of Novi Sad, Serbia. She got PhD degree at the University of Novi Sad in 1981. In 2015 she finished her second dissertation at the Hungarian Academy of Sciences.

She is member of the International Federation of Theory of Mechanisms and Machines IFToMM. She was the President of the Society of Mechanics of Vojvodina, President of the Society for Vibration Control and Protection, President of the Yugoslav Society of Mechanics.

She published three English language monographs, as well as several textbooks in Serbian.

She is member of the Editorial Board of Theoretical and Applied Mechanics and Facta Universitatis, Ser. Mechanics, Automatic Control and Robotics, associated editor of Mechanism and Machine Theory and Journal of Applied Mathematics.

PREFACE

1. INTRODUCTION

2. LINEAR OSCILLATOR AND A NON-IDEAL ENERGY SOURCE

2.1. Simple degree of freedom oscillator coupled with a non-ideal energy source

2.1.1. Analytical solving procedure

2.1.2. Sommerfeld effect

2.1.3. Model analogy and numerical simulation

2.1.4. Stability analysis

2.2. Oscillator with clearance coupled with a non-ideal source

2.2.1. Model of the system

2.2.2. Transient motion of the system

2.2.3. Steady-state motion of the system

2.2.4. Chaotic motion

2.2.5. Chaos control

2.3. Conclusion

2.4. References

3. NONLINEAR ONE-DEGREE-OF-FREEDOM OSCILLATOR INTERACTING WITH A NON-IDEAL ENEGY SOURCE

3.1. Stable Duffing oscillator coupled with a non-ideal energy source

3.2. Bistable Duffing oscillator coupled with a non-ideal energy source

3.3. Pure strong nonlinear oscillator coupled with a non-ideal energy source

3.4. Conclusion

3.5. References

4. NON-IDEAL VIBRATING SYSTEMS WITH DAMPERS

4.1. System with electromechanical vibration absorber

4.2. System with magnetically levitated vibrating system

4.3. System with magnetic rheological damper (MRD)

4.4. References

5. TWO-DEGREE-OF-FREEDOM OSCILLATOR INTERACTING WITH A NON-IDEAL ENEGY SOURCE

5.1. Non-ideal energy source on the vibrating foundation

5.2. Non-ideal vibrating system coupled to a magneto-rheological damper

5.3. References

6. VIBRATION OF A NON-IDEAL ROTOR SYSTEM

7. PORTAL FRAME SUPPORTING NON-IDEAL ENERGY SOURCES

7.1. Regular and chaotic motion in a non-ideal portal frame system

7.2. Self-synchronization of two non-ideal sources supported by a portal frame

7.3. Self-synchronization of four non-ideal exciters

7.4. References

8. APPLICATION OF NON-IDEAL SYSTEMS IN ENERGY HARVESTING

8.1. Non-ideal energy harvesting

8.2. Energy harvesting system with piezoelectric coupling

8.3. Non-ideal portal frame in energy harvester

9. APPENDIX

INDEX

In this book the dynamics of the non-ideal oscillatory system, in which the excitation is influenced by the response of the oscillator, is presented. Linear and nonlinear oscillators with one or more degrees of freedom interacting with one or more energy sources are treated. This concerns for example oscillating systems excited by a deformed elastic connection, systems excited by an unbalanced rotating mass, systems of parametrically excited oscillator and an energy source, frictionally self-excited oscillator and an energy source, energy harvesting system, portal frame - non-ideal source system, non-ideal rotor system, planar mechanism - non-ideal source interaction. For the systems the regular and irregular motions are tested. The effect of self-synchronization, chaos and methods for suppressing chaos in non-ideal systems are considered. In the book various types of motion control are suggested. The most important property of the non-ideal system connected with the jump-like transition from a resonant state to a non-resonant one is discussed. The so called 'Sommerfeld effect', resonant unstable state and jumping of the system into a new stable state of motion above the resonant region is explained. A mathematical model of the system is solved analytically and numerically. Approximate analytical solving procedures are developed. Besides, simulation of the motion of the non-ideal system is presented. The obtained results are compared with those for the ideal case. A significant difference is evident.

The book aims to present the established results and to expand the literature in non-ideal vibrating systems. A further intention of the book is to give predictions of the effects for a system where the interaction between an oscillator and the energy source exist. The book is targeted at engineers and technicians dealing with the problem of source-machine system, but is also written for PhD students and researchers interested in non-linear and non-ideal problems.