Topographical and barrier influences on hydroelastic response of an elastic plate floating in a two-layer fluid

Abstract

The effect of bottom topography and a surface-piercing porous barrier on the hydroelastic response of an elastic plate floating on a two-layer fluid with variable bottom topography is studied using small amplitude wave theory. As a mathematical tool, Galerkin’s single-mode approximation for waves in each layer is used for variable bottom topography, while the method of eigenfunction expansion is applied for the fluid region of a uniform bottom. In the variable bottom topography, a system of differential equations is solved. By applying matching conditions, jump conditions, and the appropriate boundary conditions, the solution is expressed as an algebraic linear system from which all the unknown constants are computed. The effects of different parameters related to the fluid, bottom topography, and porous barrier on the bending moment, shear force, and the deflection of an elastic plate are explored. The variations in the bending moments, shear forces, and plate deflection with respect to fluid density are found to be in opposite trends, caused by surface and interfacial waves, respectively. Further, as the density ratio becomes closer to one, the bending moments, shear forces, and plate deflection tend to diminish for interfacial waves. The plate is least deformed by surface and interfacial waves in the case of a concave down and a plane sloping bottom, respectively. This deformation can further be reduced by using suitable barriers as reported in this investigation. The observations may be useful in analysing the response of very large floating structures to the presence of undulating bottoms.