Impact of a planar flexible bar with geometrical discontinuities of the first kind

A model is presented for the impact of a multiple-angled flexible bar in planar motion. The model consists of a system of nonlinear differential equations that considers the multiple collisions as well as frictional effects at the contacting end, and allows one to predict the rigid and elastic body motion after the impact. The mode functions are selected such that the method can be made computationally as simple as possible, without compromising accuracy. To describe the impact between the elastic bar and the rigid surface, the classical Hertzian contact theory and elasto-plastic indentation theory are used. Particular emphasis is placed on the geometry of the bar because the unit tangent vector and the unit normal vector have first-order discontinuities. Analytical and experimental results are compared to establish the accuracy of the model.