Interaction between surface gravity wave and submerged horizontal flexible structures

Abstract

Interactions between surface gravity wave and submerged horizontal flexible structures are studied under the assumption of small amplitude water wave theory and structural response. The generalized dispersion relation associated with surface gravity wave interaction with submerged horizontal flexible plate is analyzed to understand the characteristics of the two propagating modes due to the presence of the free surface and submerged horizontal plate. The phase and group velocities are studied in order to analyze the effect of submerged flexible plate on gravity wave motion. The expansion formulae based on Green’s function technique and eigenfunction expansion method using Fourier transform with appropriate orthogonal mode-coupling relation associated with surface gravity wavemaker problems are derived and compared in both the cases of water of finite and infinite depths. The usefulness of the expansion formulae is demonstrated by deriving the solution for surface gravity wave interaction with submerged articulated flexible plate in water of finite depth. Several numerical results on reflection and transmission coefficients related to submerged flexible plate are presented in order to understand the effect of submerged flexible structure on surface wave motion in different cases.