Discontinuous dynamics of a class of oscillators with strongly nonlinear asymmetric damping under a periodic excitation

Abstract Starting from the quarter car suspension system, the discontinuous dynamics of a general class of strongly nonlinear single degree of freedom oscillators are investigated using the flow switchability theory of the discontinuous dynamical systems. The characteristic of this oscillator is that they possess piecewise linear damping properties, which can be expressed in a general asymmetric form. More specifically, the viscous and constant damping properties appearing in the equation of motion depend on the velocity direction. Different domains and boundaries are defined according to the discontinuity. Based on above domains and boundaries, the analytical conditions for motion switchability at the velocity boundary in such oscillators are developed to understand the motion switching mechanism. To describe different motions in domains, the generic mappings and mapping structures are introduced. Based on the appropriate mapping structures, the periodic motions of such discontinuous systems are predicted analytically. Specified periodic and grazing motions for the quarter car model are given through the displacement, velocity and forces responses to illustrate the analytical criteria of complex motions. However, the periodic motions with switching for such nonlinear oscillators cannot be obtained from the traditional analysis, like the perturbation and harmonic balance method. Moreover, the present analysis can be extended to cover wider classes of dynamical systems, like mechanical oscillators with variable stiffness and damping properties.

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