Elastoplastic impact of a long rod on a flexible large plate

Unlike impacting a rigid substrate, a rod impacting a flexible plate generates additional dissipation in the bending wave propagating through the plate. In this paper, we present an theoretical model to study the vertical impact of a slender elastoplastic rod impacting a large flexible plate. The longitudinal vibration of the rod is described by the one-dimensional wave equation, and the vibration of the impacted plate is described by the Zener governing equation. An equivalent spring model is used to describe the plastic contact between the elastoplastic hemispherical end and the plate, thus relating the dynamics of the rod and the plate. Laplace transform is used to solve the coupled equations, and the theoretical solution in Laplace space is obtained. The displacement and velocity histories along the rod and the motion of the plate predicted by the theoretical model agree well with the corresponding finite element simulations. In addition, the proposed theoretical model is also applicable when the substrate turns rigid.