In this paper, from the local theory of flow at the corner in discontinuous dynamical systems, obtained are analytical conditions for switching impact-alike chatter at corners. The objective of this investigation is to find the dynamics mechanism of border-collision bifurcations in discontinuous dynamical systems. Multivalued linear vector fields are employed, and generic mappings are defined among boundaries and corners. From mapping structures, periodic motions switching at the boundaries and corners are determined, and the corresponding stability and bifurcations of periodic motions are investigated by eigenvalue analysis. However, the grazing and sliding bifurcations are determined by the local singularity theory of discontinuous dynamical systems. From such analytical conditions, the corresponding parameter map is developed for periodic motions in such a multivalued dynamical system in the single domain with corners. Numerical simulations of periodic motions are presented for illustrations of motions complexity and catastrophe in such a discontinuous dynamical system.
Skip Nav Destination
Article navigation
November 2017
Research-Article
Complex Dynamics of Bouncing Motions at Boundaries and Corners in a Discontinuous Dynamical System
Jianzhe Huang,
Jianzhe Huang
Department of Energy and Power Engineering,
Harbin Engineering University,
Harbin 150001, China
Harbin Engineering University,
Harbin 150001, China
Search for other works by this author on:
Albert C. J. Luo
Albert C. J. Luo
Department of Mechanical and
Industrial Engineering,
Southern Illinois University Edwardsville,
Edwardsville, IL 62026-1805
e-mail: aluo@siue.edu
Industrial Engineering,
Southern Illinois University Edwardsville,
Edwardsville, IL 62026-1805
e-mail: aluo@siue.edu
Search for other works by this author on:
Jianzhe Huang
Department of Energy and Power Engineering,
Harbin Engineering University,
Harbin 150001, China
Harbin Engineering University,
Harbin 150001, China
Albert C. J. Luo
Department of Mechanical and
Industrial Engineering,
Southern Illinois University Edwardsville,
Edwardsville, IL 62026-1805
e-mail: aluo@siue.edu
Industrial Engineering,
Southern Illinois University Edwardsville,
Edwardsville, IL 62026-1805
e-mail: aluo@siue.edu
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 1, 2016; final manuscript received April 1, 2017; published online September 7, 2017. Assoc. Editor: Tomasz Kapitaniak.
J. Comput. Nonlinear Dynam. Nov 2017, 12(6): 061014 (11 pages)
Published Online: September 7, 2017
Article history
Received:
December 1, 2016
Revised:
April 1, 2017
Citation
Huang, J., and Luo, A. C. J. (September 7, 2017). "Complex Dynamics of Bouncing Motions at Boundaries and Corners in a Discontinuous Dynamical System." ASME. J. Comput. Nonlinear Dynam. November 2017; 12(6): 061014. https://doi.org/10.1115/1.4036518
Download citation file:
Get Email Alerts
A robust numerical approach for the fractional Polio model by the Genocchi wavelet collocation method
J. Comput. Nonlinear Dynam
Generation of a Multi-wing Hyperchaotic System with a Line Equilibrium and its Control
J. Comput. Nonlinear Dynam
Bifurcation analysis and control of traffic flow model considering the impact of smart devices for drivers
J. Comput. Nonlinear Dynam
Related Articles
Path-Following Bifurcation Analysis of Church Bell Dynamics
J. Comput. Nonlinear Dynam (November,2017)
Interaction Between Coexisting Orbits in Impact Oscillators
J. Comput. Nonlinear Dynam (November,2017)
Feedback Control of Grazing-Induced Chaos in the Single-Degree-of-Freedom Impact Oscillator
J. Comput. Nonlinear Dynam (January,2018)
A Piecewise-Linear Approximation of the Canonical Spring-Loaded Inverted Pendulum Model of Legged Locomotion
J. Comput. Nonlinear Dynam (January,2016)
Related Proceedings Papers
Related Chapters
Dynamic Behavior in a Singular Delayed Bioeconomic Model
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)
Two-Dimension Simulation of a Red Blood Cell Partitioning in Microvascular Bifurcation
International Conference on Software Technology and Engineering (ICSTE 2012)
Ultra High-Speed Microbridge Chaos Domain
Intelligent Engineering Systems Through Artificial Neural Networks, Volume 17