Transient Responses of Repeated Transverse Impacts on Beams

In this paper, the eigenfunction expansion method combined with local contact models are presented to analyze the repeated impact behaviors between the sphere and the beam. The simulations are verified with the experimental results of a simply-supported beam struck 91 times by a sphere. In order to clarify the validity of the eigenfunction expansion method to solve the repeated transverse impacts on beams, the simulation results of the spring-mass method are also compared with the experiments. It shows that with appropriate contact models, the eigenfunction expansion method can predict agreeable results with the experimental results, especially the impact behaviors (including the accumulated permanent indentation, the coefficient of restitution and the separation velocity of the sphere) representing energy dissipations, due to the consideration of structural vibrations, local impact behaviors, as well as the wave propagations. The comparisons between the eigenfunction expansion method and the spring-mass model show that the wave propagations are important for energy dissipations, which cannot be neglected in flexible structure impacts. The studies are important for the analysis of repeated impact response of beam structures.