Vibro-impact Dynamics.
Title:
Vibro-impact Dynamics.
Author:
Luo, Albert C. J.
ISBN:
9781118402900
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (269 pages)
Contents:
VIBRO-IMPACT DYNAMICS -- Contents -- Preface -- 1 Introduction -- 1.1 Discrete and Discontinuous Systems -- 1.1.1 Discrete Dynamical Systems -- 1.1.2 Discontinuous Dynamical Systems -- 1.2 Fermi Oscillators and Impact Problems -- 1.3 Book Layout -- 2 Nonlinear Discrete Systems -- 2.1 Definitions -- 2.2 Fixed Points and Stability -- 2.3 Stability Switching Theory -- 2.4 Bifurcation Theory -- 3 Complete Dynamics and Fractality -- 3.1 Complete Dynamics of Discrete Systems -- 3.2 Routes to Chaos -- 3.2.1 One-Dimensional Maps -- 3.2.2 Two-Dimensional Systems -- 3.3 Complete Dynamics of the Henon Map -- 3.4 Similarity and Multifractals -- 3.4.1 Similar Structures in Period Doubling -- 3.4.2 Fractality of Chaos via PD Bifurcation -- 3.4.3 An Example -- 3.5 Complete Dynamics of Logistic Map -- 4 Discontinuous Dynamical Systems -- 4.1 Basic Concepts -- 4.2 G-Functions -- 4.3 Passable Flows -- 4.4 Non-Passable Flows -- 4.5 Grazing Flows -- 4.6 Flow Switching Bifurcations -- 5 Nonlinear Dynamics of Bouncing Balls -- 5.1 Analytic Dynamics of Bouncing Balls -- 5.1.1 Periodic Motions -- 5.1.2 Stability and Bifurcation -- 5.1.3 Numerical Illustrations -- 5.2 Period-m Motions -- 5.3 Complex Dynamics -- 5.4 Complex Periodic Motions -- 6 Complex Dynamics of Impact Pairs -- 6.1 Impact Pairs -- 6.2 Analytical, Simplest Periodic Motions -- 6.2.1 Asymmetric Period-1 Motion -- 6.2.2 Stability and Bifurcation -- 6.2.3 Numerical Illustrations -- 6.3 Possible Impact Motion Sequences -- 6.4 Grazing Dynamics and Stick Motions -- 6.5 Mapping Structures and Periodic Motions -- 6.6 Stability and Bifurcation -- 7 Nonlinear Dynamics of Fermi Oscillators -- 7.1 Mapping Dynamics -- 7.2 A Fermi Oscillator -- 7.2.1 Absolute Description -- 7.2.2 Relative Description -- 7.3 Analytical Conditions -- 7.4 Mapping Structures and Motions -- 7.4.1 Switching Sets and Generic Mappings.
7.4.2 Motions with Mapping Structures -- 7.4.3 Periodic Motions and Local Stability -- 7.5 Predictions and Simulations -- 7.5.1 Bifurcation Scenario -- 7.5.2 Analytical Prediction -- 7.5.3 Numerical Simulations -- Appendix 7.A -- References -- Index.
Abstract:
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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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