Mass-plate impact parameters for the elastic range

Abstract

When an impact load is applied laterally to a plate, the deflection gradually spreads over time until the entire plate radius is affected. The determination of effects for a short-duration impact presents substantial mathematical difficulties. The normal-mode superposition is not only awkward but it does not lead to closed-form solutions. Some of the past works gave a possibility of such a solution by assuming a certain flexural wave spreading from the impact point. The complexity involved in that was simplified in this paper. This main part of this work is based on a shear wave approach, by relating the lateral stiffness to the propagation of a shear wave from impact point. This, along with some other simplifications, makes it possible to obtain the peak contact force by using compact expressions. The development is limited to impactor mass not exceeding one-half of the plate mass. The evaluation of rebound velocity or the coefficient of restitution was successfully resolved for only a limited range of parameters. The other subtopic is the quantification of the contact problem itself, which is nonlinear by nature. A transparent method of linearization is proposed, based either on experiment or on Hertzian formulation. The results presented in this paper are compared with the answers from finite-element simulations, physical experiments and with some cases available from literature.