Scattering of water waves by an inclined elastic plate in deep water

The interaction of linear water waves with an inclined elastic plate as a breakwater is analyzed when it is clamped at the upper end and moored at the lower end. The assumption of Euler-Bernoulli beam model for the plate allows to obtain the normal derivative of the potential function across the plate boundary. On the other hand, using Green's integral theorem, another expression is evaluated for the same. The comparison between these two forms provides a hypersingular integral equation of the first kind in the potential difference across the plate, which is solved by the expansion-collocation method. The solution of the hypersingular integral equation is used to find the reflection and the transmission coefficients and the hydrodynamic force. The results are presented for different inclination angle, different submergence depth of the plate, variable length and different flexural rigidity of the plate.