Hypersingular Integral Equation Approach for Hydroelastic Analysis of a Submerged Elastic Plate

Abstract

In this paper, obliquely incident surface ocean waves interaction with a horizontal submerged thin floating elastic plate is investigated in ocean water of finite depth. Firstly, a proper Green’s function associated with the physical problem is developed. Applying Green’s second identity on the upper plate and lower plate regions and using the plate conditions, the BVP is converted into a hypersingular integral equation. Most of the time, these kinds of hypersingular integral equations are solved by using some standard numerical solution techniques. But in the present case, this hypersingular integral equation is directly solved using the plate deflection in terms of summations of horizontal components of eigenfunctions related to the flexural gravity waves. In this way, a system of linear algebraic equations is obtained from the hypersingular integral equation. Further, using the plate edge conditions, some more equations involving the unknowns are obtained and solved to get the required unknowns. Variations of reflection and transmission coefficients for a wide range of physical parameters are evaluated, plotted, and analyzed.