Analytical Periodic Motions and Bifurcations in a Frictional Oscillator on Displacement-Dependent Conveyor Systems - Li, Ziyi; Luo, Albert C. J. (Journal of Vibration Testing and System Dynamics, 2026)
In this paper, dynamics of a frictional oscillator on the displacement-related belt boundary is studied. To understand dynamics of such a frictional oscillator, analytical conditions of motion switching on the nonlinear boundary are developed. For each domain, the linear oscillator solutions are given. From such solutions and motion switching conditions, periodic motions of the frictional oscillator is obtained, and numerical results give illustrations of periodic motions with switchability conditions at the boundary. From such methodology, dynamics of nonlinear frictional oscillators is studied in sequel. The analytical framework developed in this paper can be applied for discontinuous dynamical systems with state-dependent boundaries, the analytical conditions for grazing, sliding, and passable motions can be developed.