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Journal of Vibration Testing and System Dynamics 10(3) (2026) 297--312 | DOI:10.5890/JVTSD.2026.09.007

Albert C.J. Luo, Zixu Huang

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

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Abstract

In this paper, periodic motions in a periodically forced Duffing oscillator with damping switching are obtained semi-analytically through the implicit mapping method. Between system switching, specific dynamical subsystems in the switching system are continuous, which are discretized to obtain discrete implicit mappings. Based on discrete implicit mappings, specific mapping structures are employed to determine periodic motions in such a switching system, and the corresponding stability and bifurcations of periodic motions in the switching system is determined through the eigenvalue analysis. From the analytical solutions, initial conditions are chosen for numerical simulations. The numerical and analytical solutions of stable periodic motions match very well. However, for unstable periodic motions, numerical solutions move away from the analytical solutions once the computational time becomes longer. The method presented in this paper can be applied to other switched nonlinear systems, system controls and MEMS.

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