Dynamics of Mechanical Systems with Non-Ideal Excitation (eBook)

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 6
Contents 8
1 Introduction 12
References 17
2 Linear Oscillator and a Non-ideal Energy Source 20
2.1 Simple Degree of Freedom Oscillator Coupled with a Non-ideal ƒ 21
2.1.1 Analytical Solving Procedure 23
2.1.2 Steady-State Solution and Sommerfeld Effect 25
2.1.3 Model Analogy and Numerical Simulation 29
2.1.4 Stability Analysis 32
2.2 Oscillator with Variable Mass Excited with Non-ideal Source 33
2.2.1 Model of the System with Variable Mass 34
2.2.2 Model of the System with Constant Mass 36
2.2.3 Comparison of the Systems with Constant and Variable Mass 38
2.3 Oscillator with Clearance Coupled with a Non-ideal Source 41
2.3.1 Model of the System 42
2.3.2 Transient Motion of the System 44
2.3.3 Steady-State Motion of the System 48
2.3.4 Chaotic Motion 53
2.3.5 Chaos Control 55
2.4 Conclusion 56
References 57
3 Nonlinear Oscillator and a Non-ideal Energy Source 59
3.1 Nonlinear Oscillator Coupled with a Non-ideal Motor ƒ 60
3.1.1 Nonlinear Motor Torque Property 61
3.1.2 Solution Procedure in General 63
3.1.3 Steady-State Motion and Its Stability 67
3.1.4 Characteristic Points on the Steady State Curves 68
3.1.5 Suppression of the Sommerfeld Effect 69
3.1.6 Conclusion 70
3.2 Pure Nonlinear Oscillator and the Motor with Nonlinear Torque 70
3.2.1 Approximate Solution Procedure 73
3.2.2 Steady-State Motion and Its Properties 74
3.2.3 Characteristic Points 76
3.2.4 Suppression of the Sommerfeld Effect 77
3.2.5 Numerical Examples 78
3.3 Pure Strong Nonlinear Oscillator and a Non-ideal Energy Source 81
3.3.1 Model of the System 83
3.3.2 Analytical Solving Procedure 84
3.3.3 Resonant Case and the Averaging Solution Procedure 86
3.3.4 Suppression of the Sommerfeld Effect 91
3.3.5 Numerical Examples of Non-ideal Driven Pure Nonlinear Oscillators 92
3.3.6 Conclusion 100
3.4 Stable Duffing Oscillator and a Non-ideal Energy Source 101
3.4.1 Asymptotic Solving Method 103
3.4.2 Stability of the Steady State Solution and Sommerfeld Effect 105
3.4.3 Numerical Simulation and Chaotic Behavior 110
3.4.4 Chaos Control 113
3.4.5 Conclusion 115
3.5 Bistable Duffing Oscillator Coupled with a Non-ideal Source 115
3.5.1 Semi-trivial Solutions and Quenching of Amplitude 119
3.5.2 Non-trivial Solutions and Their Stability 120
3.5.3 Conclusion 122
References 126
4 Two Degree-of-Freedom Oscillator Coupled to a Non-ideal Source 131
4.1 Model of the System 132
4.2 Analytical Solution 134
4.2.1 Steady-State Motion 137
4.2.2 Stability Analysis 139
4.3 Special Cases 140
4.3.1 Resonance Frequencies in Orthogonal Directions Are Equal 140
4.3.2 Resonance Frequency in One Direction Is Half of the Resonance frequency in Other Direction 144
4.4 Numerical Simulation 147
4.5 Conclusions 149
References 150
5 Dynamics of Polymer Sheets Cutting Mechanism 151
5.1 Structural Synthesis of the Cutting Mechanism 153
5.1.1 Comparison of the Simple, Eccentric and Two Slider-Crank mechanisms 155
5.2 Kinematics of the Cutting Mechanism 156
5.3 Dynamic Analysis of the Mechanism with Rigid Support 157
5.3.1 Mathematical Model of the Mechanism 157
5.3.2 Numerical Simulation 162
5.3.3 Analytical Consideration 163
5.3.4 Comparison of Analytical and Numerical Results 165
5.4 Dynamics of the Cutting Mechanism with Flexible Support ƒ 165
5.4.1 Mathematical Model of Motion of the Cutting Mechanism 166
5.4.2 Ideal Forcing Conditions 171
5.4.3 Non-ideal Forcing Conditions 173
5.4.4 Non-stationary Motion 178
5.5 Conclusion 180
References 181
6 Non-ideal Energy Harvester with Piezoelectric Coupling 183
6.1 Constitutive Equation of the Piezoceramic Material 185
6.2 Harvesting System with Ideal Excitation 186
6.2.1 Analytical Procedure 189
6.2.2 Harvester with Linear Piezoelectricity 192
6.2.3 Harvester with Nonlinear Piezoelectricity 195
6.3 Harvesting System with Non-ideal Excitation 197
6.3.1 Model of the Non-ideal Mechanical System with Harvesting Device 197
6.3.2 Analytical Solving Procedure 202
6.3.3 Steady-State Motion 203
6.3.4 Harvested Energy 206
6.3.5 Comparison of the Analytical and Numerical Solutions 207
6.3.6 Linear Energy Harvester 209
6.3.7 Nonlinear Energy Harvesting 210
6.3.8 Conclusion 210
6.4 Harvester with Exponential Type Non-ideal Energy Source 211
6.4.1 Numerical Simulation Results 213
6.4.2 Linear Energy Harvesting 214
6.4.3 Nonlinear Energy Harvesting 215
6.4.4 Chaos in the System 216
6.4.5 Control of the System 217
6.4.6 Conclusion 219
6.5 Non-ideal Portal Frame Energy Harvester Controlled with a Pendulum 221
6.5.1 Numerical Simulation 224
6.5.2 Conclusion 228
References 228
7 Instead Conclusions: Emergent Problems in Nowadays and Future Investigation 230
Index 235