The fundamental solution of Mindlin plates with damping in the Laplace domain and its applications

Abstract

In this paper, a fundamental solution for the Mindlin plate theory with damping is derived in the Laplace transform domain first time. The applications of this fundamental solution are demonstrated by the method of fundamental solution (MFS). All variables in the time domain can be obtained by the Durbin's Laplace transform inversion method. Numerical examples demonstrate the accuracy of the MFS and comparisons have been made with analytical solutions. To model the cutting machining process, a moving concentrated force on the plate has been investigated. The proposed MFS is shown to be simple to implement and gives satisfactory results for the shear deformable plate under dynamic loads with damping.