Analysis of Vibro-Impact Dynamical System Using Piecewise Linear Vector Fields

Abstract

An analysis of the dynamic responses has been developed for all piecewise linear single-degree-of-freedom systems with boundaries for only displacement by applying analyses based on piecewise linear vector fields. Furthermore, a generalized solution methodology has been proposed for piecewise linear systems with boundaries for both displacement and time such as the system with parameters which give rise to separations due to clearances or backlash and for rotating machinery system with boundaries for both displacement and velocity. In this paper, this methodology was developed for analyzing dynamic responses of two vibro-impact systems: one with stops at both sides and another with a stop only at one side. In matrix representation for these systems, state variables can explicitly be expressed at each region as a function of the time when an orbit hits the stop. The time can be determined by the Brent method, and periodic solutions can then be obtained. Analytical solutions are validated on vibro-impact systems by using conventional method.