On discontinuous dynamics of a 2-DOF friction-influenced oscillator with multiple elastic constraints

In this paper, the discontinuous dynamical behaviors in a 2-DOF (two-degree-of-freedom) friction-influenced oscillator with multiple elastic constraints are investigated by using flow switchability theory of discontinuous dynamical systems. The mechanical model is composed of two masses driven by periodic forces, which are on the two conveyor belts with constant speeds separately and are connected by two linear springs and two dampers. Both the same springs are fixed on both sides of the first mass. Because of the mutual effect between the two masses and the elastic constraints on both sides of the first mass, the following five cases should be considered: both the masses have nonsliding motion; one of the two masses has sliding motion; both the masses have sliding motion simultaneously; and the first mass with elastic constraints has stick motion. Different domains and boundaries for such system are defined based on the friction discontinuity and multiple elastic constraints, and the state vectors and field vectors of such system are introduced. Based on the above domains and boundaries, the analytical conditions for passable motion, sliding motion, grazing motion and stick motion in the friction induced system are obtained by means of G-functions on the corresponding boundaries. The mapping structures are presented and the periodic motions of such system are described by the basic mappings. Finally, the time histories of displacement, velocity, G-functions and the corresponding trajectories in phase plane for the two masses are illustrated numerically for a better understanding of the complex dynamical behaviors of such system. This investigation can help us use or control motion of such a friction-influenced oscillator in industry, and has important significance in the optimization design of machinery with friction, impact and multiple constraints.