Hydroelastic interaction between water waves and an array of circular floating porous elastic plates

A theoretical model based on linear potential flow theory and an eigenfunction matching method is developed to analyse the hydroelastic interaction between water waves and multiple circular floating porous elastic plates. The water domain is divided into the interior and exterior regions, representing the domain beneath each plate and the rest, which extends towards infinity horizontally, respectively. Spatial potentials in these two regions can be expressed as a series expansion of eigenfunctions. Three different types of edge conditions are considered. The unknown coefficients in the potential expressions can be determined by satisfying the continuity conditions for pressure and velocity at the interface of the two regions, together with the requirements for the motion/force at the edge of the plates. Apart from the straightforward method to evaluate the exact power dissipated by the array of porous elastic plates, an indirect method based on Green's theorem is determined. The indirect method expresses the wave-power dissipation in terms of Kochin functions. It is found that wave-power dissipation of an array of circular porous elastic plates can be enhanced by the constructive hydrodynamic interaction between the plates, and there is a profound potential of porous elastic plates for wave-power extraction. The results can be applied to a range of floating structures but have special application in modelling energy loss in flexible ice floes and wave-power extraction by flexible plate wave-energy converters.