Periodic Motion for an Oblique Impact System with Single Degree of Freedom

Abstract

Oblique impact is a common phenomenon in engineering. The appearance of oblique impact will make the system strongly nonlinear and nonsmooth. In this paper, the period N−n motion of an oblique impact system with single degree of freedom is investigated by the theory of discontinuous dynamical system. The analytical conditions for the existence and local stability of the period N−n motion are obtained. All of these are under the assumption that the mass moved with very small angular amplitude. Once such an assumption was not true, the method above would be invalid. The discrete mapping method is used to solve this problem. The analytical conditions for the existence, the local stability of the period N−n motion are given through the discrete mapping method. The numerical simulation shows that the oblique impact will make the dynamic behavior of a single degree of freedom system more complex.