Dynamic behaviour of elastic-plastic free-free beams subjected to impulsive loading

A dynamic analysis of an elastic-plastic free-free beam subjected to impact by a projectile at the mid-span or to triangularly distributed impulsive loading along the span is presented. Attention is focused on the dynamic behaviour of the beam in the early, transient stage of the response. Details of the interactions between the plastic flexural wave and the elastic flexural wave reflected from the free ends are described, which assist in understanding how the elastic effect modifies the deformation history of a beam and finally leads to a somewhat different configuration from that based on a rigid-perfectly plastic model. The partitioning of the energy in the deformed beam is also examined and a rigid-plastic model with a rotational elastic-plastic spring at the mid-span of the beam is proposed in order to estimate the proportions of elastic energy and plastic dissipation. To verify the theoretical predictions, a group of high-speed photographs obtained experimentally for central impact of a free-free beam is presented and compared with the numerical results on the instantaneous profiles of the beam.