Water wave scattering by an elastic plate floating in an ocean with a porous bed

The problem of water wave scattering by a thin horizontal elastic plate (semi-infinite as well as finite) floating on an ocean of uniform finite depth in which the ocean bed is composed of porous material of a specific type is analyzed. The method of eigenfunction expansion is used in the mathematical analysis and the quantities of physical interest, namely the reflection and transmission coefficients, are obtained. Numerical estimates for these coefficients are obtained for different values of the parameter describing the porosity of the ocean bed and for different edge conditions of the elastic plate. The edge conditions considered here involve (i) a free edge, (ii) a simply-supported edge and (iii) a built-in edge. From the numerical results it is observed that for free edge condition, the porosity of the ocean bed has little effect on the reflection and transmission coefficient for both the cases of semi-infinite and finite elastic plate. The energy identity related to reflection and transmission coefficients in a porous bed is derived and is used as a partial check on the correctness of the numerical results for the semi-infinite elastic plate.