Spatial Variation of the Coefficient of Restitution for Frictionless Impacts on Circular Beams

Abstract

The spatial variation of the coefficient of restitution for frictionless impacts along the length of a circular beam is investigated using a continuous impact model. The equations of motion are obtained using the finite element method and direct time integration is used to simulate the collision on a fast time scale. For collision of a pinned beam with a fixed cylinder, the spatial variation of the coefficient of restitution, impulse magnitude, duration of collision, energetics, and the role of damping are investigated. In the absence of significant external damping, the kinematic and kinetic definitions of the coefficient of restitution provide identical results. Experiments validate the results from simulation which indicate that the coefficient of restitution is sensitive to the location of impact.