Simulation of Longitudinal Impact Waves Using Time Delayed Systems

Abstract

In this paper, it is shown that some classic longitudinal impact problems can be solved satisfactorily with time delayed systems. As an example, a sphere colliding with a fixed rod with finite length is discussed in detail. Since it takes a finite time for a wave propagating from one position to another position, the longitudinal impact wave is naturally modeled by a time delay system. Numerical simulation shows some interesting phenomena and experimental results have validated the model with time delay. It is shown that for the computation of Poisson’s coefficient of restitution in multibody dynamics, the decomposition of the contact into the compression phase and the expansion phase must either be specified by whether the contact force increases or decrease or by whether the relative displacement increases or decreases. In the first case, the coefficient of restitution determined from the time history of the contact force could be greater than one. In the other case, the duration of contact determined from the relative displacement of the colliding bodies may be wrong as discussed in the paper.