Multiple impact of beam-to-beam

Based on the rigid-plastic string model, the problem of a beam impacted sequentially by numerous beams with a high velocity is investigated using the wave propagation approach. Attention is focused on the response of the stricken beam. The closed-form expressions for deflection and tensile strain are obtained in the double impact case. In the multiple impact case, a general recursion formula for the tensile strain as a function of the number of the striking beam is derived. By assuming the tensile necking failure mode, the critical impact velocity to fracture the stricken beam is predicted with the impact number specified. Alternatively, with the impact velocity given, the critical impact number of the striking beam is determined. Asymptotic analyses for two limiting cases with infinite and infinitesimal time interval are performed.