Comparison of several numerical methods for mechanical systems with impacts
Résumé
The modellization of mechanical systems with non-linearities of impact type leads to discontinuities in the velocity. In this paper, we study some numerical methods adapted to the occurrence of such discontinuities from a single-degree-of-freedom vibro-impact system. Theoretical results of consistency are given for numerical methods valid for smooth ordinary differential equations, with several kinds of procedures for approximating impact times. The algorithms are applied to classical Newmark and Runge-Kutta schemes, and the numerical behaviour is investigated for two categories of periodic response, either with finite or infinite number of impacts per cycle. These numerical methods are compared to a scheme without explicit computation of impact times. We show that high orders of convergence can be obtained with appropriate schemes, and we discuss the time of computation needed in each case.