Impact response of orthotropic composite plates predicted from a one-parameter differential equation

Abstract

This paper presents an approximate analytical solution for the dynamic response of an infinite specially orthotropic plate impacted by an impactor with a semispherical tip. Thus, the solution is valid for low mass impacts. The analysis is an extension and rederivation of a solution for isotropic plates proposed by Zener. The analysis assumes a Hertzian contact law and is based on Kirchhoff's plate equation. The plate response is expressed in terms of contact force, contact pressure, central displacement, central curvature, and size of the impact affected area. The response is computed from a dimensionless differential equation in time, which is only dependent on the inelasticity parameter lambda. Lambda is a function of the impact velocity and variables describing the impactor and the plate. For a given lambda, the response can be interpolated from the solution plots for a number of representativ e values of lambda. Results computed from the model are compared with published numerical analyses and a number of experiments, and a close agreement is noted. Finally, the analysis shows the time-dependent velocity of a flexural wave propagating from the impact center.