Comparison of several numerical methods for mechanical systems with impacts

The modellization of mechanical systems with non-linearities of impact type leads to discontinuities in the velocity. In this paper, we study some num erical methods adapted to the occurrence of such discontinuities from a sin gle-degree-of-freedom vibro-impact system. Theoretical results of consisten cy are given for numerical methods valid for smooth ordinary differential e quations, with several kinds of procedures for approximating impact times. The algorithms are applied to classical Newmark and Runge-Kutta schemes, an d the numerical behaviour is investigated for two categories of periodic re sponse, either with finite or infinite number of impacts per cycle. These n umerical methods are compared to a scheme without explicit computation of i mpact times. We show that high orders of convergence can be obtained with a ppropriate schemes, and we discuss the time of computation needed in each c ase. Copyright (C) 2001 John Wiley & Sons, Ltd.