Approximate boundary conditions for a fluid-loaded elastic plate

Abstract

Approximate boundary conditions for an infinite elastic layer immersed in a fluid are derived. By using series expansions in the thickness coordinate of the plate fields, the displacements fields are eliminated, adopting the three-dimensional equations of motion. The sums and differences of the boundary pressure fields and their normal derivatives are related through a set of approximate boundary conditions, one symmetric and one antisymmetric. These equations involve powers in the layer thickness together with partial derivatives with respect to time as well as the spatial variables in the plate plane. The approximate boundary conditions can be truncated to an arbitrary order, and explicit relations are presented including terms of order five. Comparisons are made with effective boundary conditions using classical plate theories. The numerical examples involve reflection and transmission of plane waves incident on the plate at different angles, as well as the pressure fields due to a line force. Three fluid-loading cases are studied: modest, heavy, and light loadings. The results using truncated approximate boundary conditions are compared to exact and classical plate solutions. The examples show that the accuracies of the power series approximations of order three and higher are very good in the frequency interval considered.