Barrier and bottom topography effects on hydroelastic response of floating elastic plate in a two-layer fluid

Abstract

The prime intention of this article is to investigate the effect of variable bottom topography and a bottom-sitting porous barrier on the hydroelastic response of an elastic plate floating on a two-layer fluid using small amplitude wave theory. Galerkin's single-mode approximation in each layer for variable bottom topography and the method of eigenfunction expansion for the fluid region of uniform bottom topography are used as mathematical tools to detail the phenomena. 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 evaluated. The effects of different parameters related to the fluid, bottom topography, and porous barrier on the bending moment, shear force, and 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 bottom effect on bending moments, shear forces, and plate deflection is minimal due to surface waves but significant due to interface waves with maximum amplitude in a concave up bottom. The plate deformation can be further reduced using a suitable barrier, as investigated in this article. The findings hold good potential for furthering our understanding of installing an elastic plate in a stratified fluid with fluctuating water depth.