Surface wave scattering by an elastic plate submerged in water with uneven bottom

Wave interaction with a vertical elastic plate in presence of undulating bottom topography is considered, assuming linear theory and utilizing simple perturbation analysis. First order correction to the velocity potential corresponding to the problem of scattering by a vertical elastic plate submerged in a fluid with a uniform bottom is obtained by invoking the Green’s integral theorem in a suitable manner. With sinusoidal undulation at the bottom, the first-order transmission coefficient (T1) vanishes identically. Behaviour of the first order reflection coefficient (R1) depending on the plate length, ripple number, ripple amplitude and flexural rigidity of the plate is depicted graphically. Also, the resonant nature of the first order reflection is observed at a particular value of the ratio of surface wavelength to that of the bottom undulations. The net reflection coefficient due to the joint effect of the plate and the bottom undulation is also presented for different flexural rigidity of the plate. When the rigidity parameter is made sufficiently large, the results for R1 reduce to the known results for a surface piercing rigid plate in water with bottom undulation