Vibrations of an ice sheet with crack under a time-periodic load

The analytic solution of the problem of vibrations of an ice sheet with a rectilinear crack floating on the surface of an ideal incompressible fluid of shallow depth under the action of a local zone of the time-periodic pressure is obtained. The ice sheet is simulated by two thin viscoelastic semiinfinite plates of different thickness. Various conditions on the crack edges are considered. Far field asymptotics are investigated and it is revealed that the predominant directions of wave propagation at an angle to the crack can be distinguished in the far field in the case of contact of two plates of different thickness. In the case of contact of identical plates, a waveguide mode propagating along the crack is excited. It is shown that the waveguide mode is the same for the plates with the free edges and the free overlap since the part of the solution symmetric about the crack is the same while the difference between the solutions is caused by the antisymmetric part of the solution.