Attenuation in hydroelastic response of floating-elastic-plate by porous membrane in two-layer fluid with bottom undulation

Abstract

The prime intention of this article is to study the effects of bottom undulation and a porous membrane barrier on the hydroelastic response of an elastic plate floating in a two-layer fluid with changing bottom topography assuming the small amplitude waves and potential flow theory. Finite and semi-infinite plates coupled with porous membrane barriers are considered in this study. As a mathematical technique, the eigenfunction expansion method along with an approximation method mild-slope are adopted for the uniform bottom and variable bottom topographies, respectively. In the variable bottom topography, a system of differential equations is solved. By using matching and jump conditions, the solution is expressed as a linear algebraic system, from which the unknown constants of interest are computed. The effects of fluid density ratio, water depth ratio, bottom topography, and porous membrane on the bending moment, shear force, and deflection of the elastic plate are studied. It is found that when the density ratio becomes closer to one, the bending moments and shear forces acting on the elastic plates tend to diminish. The variations in the bending moments, shear forces, and plate deflection with respect to changing density ratios are found to be in opposite trends caused by surface and interfacial waves, respectively. With higher tension and a less porous membrane, the bending moment, shear forces, and pate deflection are reduced. Concave-up bottoms reflect more surface wave energy, whereas concave-down bottoms reflect more interfacial wave energy. The observations made in this article may help in analyzing the response of very-large floating structures in the presence of an undulating seabed.