Vibro-impact Dynamics

Professor Luo is currently a Distinguished Research Professor at Southern Illinois University Edwardsville. He is an international renowned figure in the area of nonlinear dynamics and mechanics. For about 30 years, Dr. Luo’s contributions on nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems, (ii) Dynamical systems synchronization, (iii) Analytical solutions of periodic and chaotic motions in nonlinear dynamical systems, (iv) The theory for stochastic and resonant layer in nonlinear Hamiltonian systems, (v) The full nonlinear theory for a deformable body. Such contributions have been scattered into 13 monographs and over 200 peer-reviewed journal and conference papers. His new research results are changing the traditional thinking in nonlinear physics and mathematics. Dr. Luo has served as an editor for the Journal “Communications in Nonlinear Science and Numerical simulation”, book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr. Luo is the editorial member for two journals (i.e., IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control). He also organized over 30 international symposiums and conferences on Dynamics and Control.

• Preface Chapter 1 Introduction 11.1. Discrete and discontinuous systems 11.1.1 Discrete dynamical systems 21.1.2 Discontinuous dynamical systems 41.2 Fermi oscillator and impact problems 81.3 book layout 10References 12Chapter 2 Nonlinear Discrete Systems 192.1 Defintions 192.2 Fixed points and stability 212.3 Stability switching theory 342.4. Bifurcation theory 50References 59Chapter 3 Complete Dynamics and Fractality 613.1 Complete dynamics of discrete systems 613.2 Routes to chaos 693.2.1 One-dimensional maps 693.2.2 Two-dimensional maps 733.3 Complete Dynamics of Henon map 753.4 Simliarity and Multifractals 813.4.1 Similar Structures in period doubling 813.4.2 Fractality of chaos via PD bifurcation 863.4.3 An example 863.5 Complete dynamics of Logistic map 93References 107Chapter 4 Discontinuous Dynamical Systems 1094.1 Basic concepts 1094.2 G-functions 1124.3 Passable flows 1164.4 Non-passable flows 1214.5 Grazing flows 1354.6 Flow switching bifucations 149References 162Chapter 5 Nonlinear Dynamics of Bouncing Balls 1635.1 Analytical dynamics of bouncing balls 1635.1.1 Periodic motions 1655.1.1 Stability and bifurcations 1685.1.3 Numerical illustrations 1755.2 Period-m motions 1805.3 Complex dynamics 1875.4 Complex periodic motions 192References 200Chapter 6 Complex Dynamics of Impact Pairs 2016.1 Impact pairs 2016.2 Analytical, simplest periodic motions 2056.3 Possible impact notion sequences 2166.4 Grazing dynamics and stick motions 2206.5 Mapping structures and periodic motions 2286.6 Stabilityand bifurcation 232References 242Chapter 7 Nonlinear Dynamics of Fermi Oscillators 2437.1 Mapping dynamics 2437.2 A Fermi oscillator 2497.2.1 Absolute description 2517.2.2 Relative description 2577.3 Analytical conditions 2587.4 Mapping structures and motions 2607.4.1 Switching sets and generic mappings 2607.4.2 Motions with mapping structures 2637.4.3 Periodic motion and local stability 2657.5 Predictions and similations 2687.5.1 Bifurcation scenarios 2687.5.2 Analytical predictions 2717.5.3 Numberical illustractions 2787.6 Appendix 291References 295Subject index 297

"It provides a unified treatment on the topic with a sound theoretical base that is applicable to both continuous and discrete systems." (Zentralblatt MATH, 2016)