An Energy-Based Coefficient of Restitution for Planar Impacts of Slender Bars With Massive External Surfaces

A new method to solve the collision problems of slender bars with massive external surfaces is developed. The proposed solution accounts for the effect of impact induced vibrations and multiple collisions on the post-collision velocities of the impacting members. The approach is based on representing the vibrational energy of the bars during the collision process in terms of a nondimensional parameter, termed the elastic energy percentile. The elastic energy percentile is expressed as a simple scalar function of the drop angle and a nondimensional parameter, which encapsulates the bar geometry, material, and the stiffness of the contact surface. The elastic energy percentile is then used to develop a new momentum-based solution method. The method relies on a revised energetic coefficient of restitution that resolves the effect of impact induced vibrations on the post-collision velocities of the impacting bars. The assumptions used in the theoretical development and the outcomes predicted by the proposed method were verified by conducting a set of experiments using several bars with varying geometric and material properties.