Comparison of several numerical methods for mechanical systems with impacts.

*(English)*Zbl 1056.74059Summary: The modellization of mechanical systems with nonlinearities 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 on 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.