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Journal of Vibration Testing and System Dynamics 5(2) (2021) 131--147 | DOI:10.5890/JVTSD.2021.06.003

Siyuan Xing$^{1}$, Albert C.J. Luo$^{2}$ , Jianzhe Huang$^{3}$

$^{1}$ Department of Mechanical Engineering, California Polytechnic State University, San Luis, Obispo, CA 93401, USA

$^{2}$ Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA

$^{3}$ School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China

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Abstract

This paper presented the dynamics of an infinite-equilibrium system based on a quadratic oscillator. equilibria, stability and singularity of such an infinite equilibrium system are discussed through the local analysis, and numerical studies of the periodically perturbed infinite-equilibrium systems are completed. The infinite-equilibrium boundaries in infinite-equilibrium systems can be artificially designed to control motions in the corresponding non-infinite-equilibrium systems. Through this study, one can have a better understanding of dynamics of infinite-equilibrium nonlinear systems. The authors believe infinite-equilibrium systems will have extensive applications in science and engineering.

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