Hydroelastic Waves in an Ice-Covered Channel with Linearly Varying Ice Thickness

The solution to the problem of flexural-gravity waves in an ice-covered channel is constructed and investigated when the ice thickness varies linearly from one to another channel wall. The channel cross-section is rectangular. It is assumed that the ice-plate thickness is small as compared with the channel depth and the plate edges are frozen to the channel walls. The ice cover deflection is described within the framework of the linear theory of elastic plates, fluid flow beneath ice is assumed to be potential. The problem is solved using expansions of the plate deflection in the modes of vibration of the plate whose thickness varies linearly across the the channel width. The dispersion relations, the profiles of flexural-gravity waves across the channel, and the strain distributions in the ice cover are determined. The group and phase velocities of hydroelastic waves are found. The hydroelastic characteristics are investigated as functions of the linear coefficient of the ice thickness. The results obtained are compared with the results for the uniform ice cover.