An Analytical Method for Evaluating the Dynamic Response of Plates Subjected to Underwater Shock Employing Mindlin Plate Theory and Laplace Transforms

It is often in the interest of a designer to know the transient state of stress in a plate subjected to an underwater explosion. In this paper, an analytical method based on Taylor’s fluid-solid interaction (FSI) model, Mindlin plate theory, Laplace transform, and its inversion is proposed to examine the elastic dynamic response of a plate subjected to an underwater explosion. This analytical method includes shear deformation, the moments and membrane stress in the plate, and the FSI effect and considers a full profile of possibilities. The results of the response-time histories and the response distribution on the plate in terms of displacements and stresses from the analytical method are compared with finite element analysis (FEA) to validate this method, and the comparison indicates good agreement. Comparison of the acceleration at the center of an air-backed plate between the analytical method and the experiment from relevant literature, shows good agreements, and the analytical method and its FSI model are validated. The influence of the FSI is investigated in detail. All extreme values of the response-time histories decrease as the thickness increases for the non-FSI case. The results can be used as benchmark solutions in further research.