Complex Dynamics of Bouncing Motions on Boundaries and Corners in a Discontinuous Dynamical System

[+] Author and Article Information
Jianzhe Huang

Department of Energy and Power Engineering, Harbin Engineering University, Harbin 150001, China

Albert C.J. Luo

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA

1Corresponding author.

ASME doi:10.1115/1.4036518 History: Received December 01, 2016; Revised April 01, 2017


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 bifurcation in discontinuous dynamical systems. Multi-valued linear vector fields are employed in the discontinuous dynamical system, and generic mappings are defined among the boundaries and corners. From mapping structures, periodic motions switching on 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 in discontinuous dynamical systems. From such analytical conditions, the corresponding parameter map are developed for periodic motions in such multi-valued dynamical systems in the single domain with corners. Numerical simulations of periodic motions are presented for illustrations of motions complexity and catastrophe in the discontinuous dynamical system.

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