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Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


An Analytical Prediction of Periodic Motions in a Discontinuous Dynamical System

Journal of Vibration Testing and System Dynamics 4(4) (2020) 377--388 | DOI:10.5890/JVTSD.2020.12.006

Siyu Guo, Albert C. J. Luo

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL62026-1805, USA

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Periodic motions in a discontinuous dynamical system are studied. The discontinuous dynamical system consists of three distinct linear dynamical systems with two different circular boundaries. Analytical conditions for switching and sliding motions at the two circular boundaries are developed. From such analytical conditions, periodic motions in discontinuous dynamical systems can be determined through specific mapping structures. Illustrations give periodic motions in discontinuous dynamical systems, which are different from the continuous dynamical systems. In different domains, the motions are different, and the discontinuity of the periodic motions at the boundaries is observed, and the sliding motion on the boundaries is also a portion of periodic motion. Such periodic motions in discontinuous dynamical systems do not have any Fourier series. The methodology presented in this paper can be applied to other discontinuous dynamical systems. The circular boundaries can be treated different energy levels as control conditions in engineering systems.


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