Wave Motion in an Ice Sheet with Crack under Uniformly Moving Load

Abstract

The analytical solution to the problem of the behavior of an ice sheet with rectilinear crack under the action of uniformly moving rectangular external pressure zone simulating an air-cushion vehicle is obtained using the Wiener–Hopf technique. The ice cover is simulated by thin elastic semi-infinite plates of constant thickness floating on the surface of an incompressible fluid of finite depth. Two configurations are considered: 1) two semi-infinite plates with free edges (whose thicknesses can be different) are separated by a crack; 2) fluid is bounded by the vertical wall and the ice cover edge can be both free and frozen to the wall. In the case of the contact of plates of the same thickness, as well as in the presence of the wall, the solution is obtained in the explicit form. It is shown that in the case of the contact of identical plates with free edges, edge waveguide modes traveling along the crack are excited when the load moves at a supercritical speed. Both the wave forces acting on the moving body and the deflections of the plates are investigated for various values of the plate thicknesses and the load velocity in the sub- and supercritical regimes.