Hydroelastic Waves in a Porous Ice Plate

Within the linear theory of hydroelasticity, a two-dimensional problem of hydroelastic waves in a porous ice plate is considered. Porosity is modeled by taking into account the liquid penetration velocity proportional to the pressure gradient in the kinematic condition at the plate—liquid interface. In the initial formulation, forced oscillations caused by unsteady external pressure are considered. The solution is constructed using the Fourier transform method. A system of differential equations is obtained, the homogeneous solution of which describes time-damping hydroelastic waves. The existence of a critical value of a real-valued porosity parameter has been established, at which waves with a nonzero frequency disappear in a finite range of wave numbers. The imaginary part of the porosity affects the asymmetry of the frequency values relative to the real axis and the degree of wave attenuation. The models are compared with/without taking into account mass and hydrostatic pressure. Analytical expressions are obtained for the case of a pulse start and subsequent movement of the load at a given speed. The integrals describing the ice reaction are numerically calculated for different times.