Discontinuous dynamical behaviors in a vibro-impact system with multiple constraints

Abstract

In this paper, the discontinuous dynamical behaviors in a two-degree-of-freedom vibro-impact system with multiple constraints are investigated by using the flow switchability theory of discontinuous dynamical systems. Due to the interaction between the two masses in this discontinuous system, the following four cases are taken into account: both the masses are free-flight; one of the two masses is sticking; and both the masses are sticking. Different domains and boundaries are defined in absolute and relative coordinates based on the discontinuity caused by the impact between the masses and the constraints. From the above domains and boundaries, the analytical conditions of switching for stick motions and grazing motions in the vibro-impact system are obtained through the analysis of the corresponding vector fields and G-functions. The switching sets and four-dimensional mappings are introduced to describe different periodic motions and identify the corresponding mapping structures. Periodic motions with different mapping structures in the vibro-impact system are analytically predicted. The time histories of displacement, velocity, G-function and the corresponding trajectories in phase plane for stick, grazing and periodic motions are given to illustrate the dynamics mechanism of complex motions in such a vibro-impact system. A better understanding of the motion switching mechanism in mechanical systems with multiple constraints may be helpful for improving the efficiency of vibro-impact systems.