The hydroelastic interaction between surface gravity waves and submerged elastic plates is significantly influenced by both porous bed and plate parameters. Hence, in this study, the physical scenario is considered within the framework of linear water wave theory. Accordingly, the plates are described by thin elastic plate theory with in-plane compressive force, and the porous bed is represented through a frictional coefficient and a porosity parameter, allowing both impermeable and permeable bed conditions to be examined. Dispersion relations are derived and analyzed for real and complex values of the porous bed frictional coefficient, considering only propagating wave modes. The analysis focuses on the porosity and resistance parameter of the porous bed, as well as the plate compression and examines how they modify the hydroelastic wave behavior. The limiting case of a single-submerged plate configuration is analyzed, where the effects of porosity, resistance parameter, and plate compression on dispersion behavior, phase velocity, and group velocity are investigated. The results show that due to the porosity of the porous bed, the frequency branches become complex-valued over finite wavenumber ranges. In these ranges, the real parts of the frequency branches overlap, while their imaginary parts separate. This reflects the effects of porous bed dissipation. For the dual-submerged plate, the selective compression of both plates is shown, with different dispersion branches showing different effects on the interactions with the plate and porous bed. Time-domain simulations also demonstrate the particular characteristics of wave propagation of free surface modes and plate modes, along with the influence of compression on the plate response.
Ratnakumari et al. (2026) studied this question.