Hydroelasticity induced by the interaction of linear long waves with a submerged elastic plate over an asymmetric stepped seabed

Hydroelastic interactions between long waves and a submerged elastic plate over a stepped seabed are investigated analytically in the regime where plate deflections are comparable to the incident wave amplitude. This enables a systematic assessment of the influence of structural energy transfer on the hydrodynamic response. The fluid motion is modeled within the framework of linear potential flow theory. The mechanical behavior of the plate is described using the Kirchhoff–Love thin-plate theory, including the effect of a uniform in-plane force. Four edge constraint configurations are examined: clamped–clamped, clamped–free, free–clamped, and free–free. The analysis focuses on the behavior of the reflection coefficients, the hydrodynamic energy fluxes, and the structural energy flux exchanged with the fluid. For a highly flexible plate with length almost equal to the wavelength with one end clamped and the other free, it was found that the energy flux on the upper surface is approximately fivefold greater than that on the lower surface. In the case when the plate length is approximately the middle of the wavelength, the maximum flux energy is presented below the plate surface, which is approximately twice as large than that presented on the upper surface. This concentration of energy indicates that a submerged flexible plate can act as a passive energy-redistribution device, potentially suitable for wave-energy concentration applications. The results indicate that the edge boundary conditions, bending stiffness, in-plane force, and depth ratios have a pronounced effect on both the reflection characteristics and the partitioning of energy between fluid and structure. The proposed analytical solution is validated by comparison with classical solutions reported in the literature, showing good agreement. The formulation developed herein provides a benchmark tool for the analysis of hydroelastic behavior of submerged flexible plates, with potential applications in wave energy conversion and coastal protection design.