Enhancement of wave energy flux induced by linear long-waves–flexible plate interaction in the presence of a stepped seabed

The effects of a stepped seabed on the interaction between linear long waves and a flexible, horizontal, and submerged plate are theoretically analyzed. The reflected and transmitted wave energies, together with the wave flux energy concentrated below and above the plate, are characterized. The mechanical response of the structure is obtained from the Kirchhoff-Love thin plate theory. Wave hydrodynamics are analyzed under the assumption of potential flow theory. The geometry of the seabed can exhibit different configurations, ranging from a uniform seabed to finite and infinite steps, vertical walls, and trenches. The plate length can be much larger than or of the same order of magnitude as the wavelength. Two boundary conditions are analyzed for the edge of the plate: when they have free displacement and when they are clamped. When the plate length is of the same order of magnitude as the wavelength, the energy flow above and below it is almost equal; however, for very long plates, the most significant energy flow occurs above it. This analytical solution allows for the characterization of the effects of a stepped seabed on the energy flux enhancement induced by the long-waves–flexible plate interaction.