Buch, Englisch, 272 Seiten, Format (B × H): 173 mm x 246 mm, Gewicht: 567 g
ISBN: 978-1-118-35945-7
Verlag: Wiley
Presents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysis
Comprehensive understanding of any vibro-impact system is critically impeded by the lack of analytical tools viable for properly characterizing grazing bifurcation. The authors establish vibro-impact dynamics as a subset of the theory of discontinuous systems, thus enabling all vibro-impact systems to be explored and characterized for applications.
Vibro-impact Dynamics presents an original theoretical way of analyzing the behavior of vibro-impact dynamics that can be extended to discontinuous dynamics. All topics are logically integrated to allow for vibro-impact dynamics, the central theme, to be presented. It provides a unified treatment on the topic with a sound theoretical base that is applicable to both continuous and discrete systems
Vibro-impact Dynamics:
- Presents mapping dynamics to determine bifurcation and chaos in vibro-impact systems
- Offers two simple vibro-impact systems with comprehensive physical interpretation of complex motions
- Uses the theory for discontinuous dynamical systems on time-varying domains, to investigate the Fermi-oscillator
Essential reading for graduate students, university professors, researchers and scientists in mechanical engineering.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preface ix
1 Introduction 1
1.1 Discrete and Discontinuous Systems 1
1.1.1 Discrete Dynamical Systems 1
1.1.2 Discontinuous Dynamical Systems 4
1.2 Fermi Oscillators and Impact Problems 7
1.3 Book Layout 9
2 Nonlinear Discrete Systems 11
2.1 Definitions 11
2.2 Fixed Points and Stability 13
2.3 Stability Switching Theory 22
2.4 Bifurcation Theory 38
3 Complete Dynamics and Fractality 47
3.1 Complete Dynamics of Discrete Systems 47
3.2 Routes to Chaos 54
3.2.1 One-Dimensional Maps 54
3.2.2 Two-Dimensional Systems 58
3.3 Complete Dynamics of the Henon Map 59
3.4 Similarity and Multifractals 64
3.4.1 Similar Structures in Period Doubling 65
3.4.2 Fractality of Chaos via PD Bifurcation 68
3.4.3 An Example 70
3.5 Complete Dynamics of Logistic Map 72
4 Discontinuous Dynamical Systems 85
4.1 Basic Concepts 85
4.2 G-Functions 88
4.3 Passable Flows 91
4.4 Non-Passable Flows 95
4.5 Grazing Flows 107
4.6 Flow Switching Bifurcations 119
5 Nonlinear Dynamics of Bouncing Balls 131
5.1 Analytic Dynamics of Bouncing Balls 131
5.1.1 Periodic Motions 133
5.1.2 Stability and Bifurcation 136
5.1.3 Numerical Illustrations 140
5.2 Period-m Motions 143
5.3 Complex Dynamics 152
5.4 Complex Periodic Motions 156
6 Complex Dynamics of Impact Pairs 165
6.1 Impact Pairs 165
6.2 Analytical, Simplest Periodic Motions 168
6.2.1 Asymmetric Period-1 Motion 170
6.2.2 Stability and Bifurcation 172
6.2.3 Numerical Illustrations 175
6.3 Possible Impact Motion Sequences 179
6.4 Grazing Dynamics and Stick Motions 182
6.5 Mapping Structures and Periodic Motions 189
6.6 Stability and Bifurcation 192
7 Nonlinear Dynamics of Fermi Oscillators 203
7.1 Mapping Dynamics 203
7.2 A Fermi Oscillator 209
7.2.1 Absolute Description 210
7.2.2 Relative Description 212
7.3 Analytical Conditions 214
7.4 Mapping Structures and Motions 218
7.4.1 Switching Sets and Generic Mappings 218
7.4.2 Motions with Mapping Structures 221
7.4.3 Periodic Motions and Local Stability 223
7.5 Predictions and Simulations 226
7.5.1 Bifurcation Scenario 226
7.5.2 Analytical Prediction 229
7.5.3 Numerical Simulations 236
Appendix 7.A 248
References 253
Index 259
