Propagation of surface gravity waves by a submerged thin elastic plate beneath an ice cover

A theoretical analysis involving surface gravity waves propagation by oblique incidence wave due to a thin elastic plate submerged in finite depth water in the presence of ice cover has been studied extensively in this paper employing Green's function technique. The edges of the elastic plate are considered to be free. The boundary conditions on the elastic plate and on the ice cover are derived from the Bernoulli-Euler's beam equation. Applying Green's function technique, the boundary condition satisfied on the elastic plate is converted into integral involving the difference in velocity potentials (unknown) across the plate multiplied by an appropriate Green's function. Utilizing Green's integral theorem, the reflection and transmission energy coefficients are explained in terms of integrals involving combinations of the unknown velocity potential on the two sides of the plate, which satisfy three simultaneous integral equations and are solved numerically. The effect of different values of physical parameters, such as flexural rigidity of ice, elastic coefficient of the barrier, and height and depth of the barrier, on the numerical assessment of magnitude of reflection and transmission coefficients is explained graphically in a number of figures. The energy balance relation is satisfied numerically. The results for a rigid plate are recovered when the parameters characterizing the elastic plate are chosen negligibly small. The influence of ice cover is clearly shown in the behavior of reflection and transmission coefficients curves. The hydrodynamic force, elastic plate deflection, shear force, and shear strain of the elastic plate are analyzed and computed analytically and graphically in a number of figures to understand the effect of ice cover on the wave motion.