Comparison of Analytical and Experimental Results for Longitudinal Impacts on Elastic Rods

Abstract

In this paper, the dynamic problem of a rigid body colliding with an elastic rod is studied in some detail. Different contact theories for modeling impact responses are compared with experimental measurements. Based on an idea originally presented by Sears for collisions of two rods with rounded ends, a boundary approach combining Hertzian contact law and St. Venant's elastodynamics is developed to describe longitudinal waves in rods. It is shown that this boundary approach agrees very well with experimental results. For the simulation of long-term dynamic behavior after impact, a traditional rigid-body approach is advantageous because the elastic vibration of the rod will decay fast due to the structural damping and the elastic rod then moves like a rigid body. Hence, for modeling longitudinal impacts, it is suggested that both elastodynamics and rigid-body dynamics are combined into a two-timescale model. The short time behavior of wave propagation due to impacts is modeled using elastodynamics, and the state of the rigid-body mode is transferred to the rigid-body approach as the initial condition for the motion. The long-term behavior after impact is then computed using the rigid-body approach.