Analysis of discontinuous dynamics of a 2-DOF system with constrained spring cushions

Abstract

We investigate the dynamical characteristics of a two degrees of freedom friction oscillator with constrained spring cushions. Based on the discontinuity resulted from the rough contact surface and the nonsmoothness resulted from fixed spring, different boundaries and domains are given in phase space. The G-functions are introduced to determine whether the passable, grazing, sliding and stick motions occur on separation boundaries. The periodic orbits in such a system are predicted by using mapping dynamical theory after introducing four-dimension switching sets and basic mappings. The passable, grazing, stick, sliding and periodic motions of system are studied numerically by the velocity, displacement and G-functions responses in order to better illustrate the switching conditions of different motions. This investigation can provide effective technical support for the optimization design of system with fixed spring cushions.