Dynamic fundamental solution of dipole for Kirchhoff plate on Winkler-Pasternak foundation

Abstract

The Method of Fundamental Solution (MFS) for the thin plate resting on the Winkler-Pasternak elastic foundation under dynamic loading is proposed in this work. In traditional MFS, the double-source method is utilized with two free variables including the locations of source pint. In order to construct MFS with few free parameters, the main aim of this paper is to deduce two fundamental solutions for a concentrated force and a dipole of thin plate resting on the elastic foundation with damping by Laplace transform technique. The behaviours and performances of fundamental solutions are observed comprehensively. Time domain numerical results are obtained by the Durbin’s inverse method and the behaviours of fundamental solutions are observed comprehensively. The main novelty of this paper is the derivation of Laplace transformed fundamental solutions of the dipole of a Kirchhoff plate resting on the Winkler-Pasternak elastic foundation with the damping factor and comparisons have been made between Kirchhoff plate and Reissner/Mindlin plate theories under dynamic loadings. In order to show the accuracy of this methodology, numerical comparisons between the present work and either analytical solutions or finite element solutions are presented. Excellent agreements with both analytical solution and finite element method solution are observed.