Steady-State Motion of a Load on an Ice Cover with Linearly Variable Thickness in a Channel

The paper considers the visco-elastic response of the ice cover in a channel under an external load moving with constant speed along the center line. The channel has a rectangular cross-section with a finite depth and width. The fluid in the channel is inviscid and incompressible and its motion is potential. The fluid is covered by a thin sheet of ice frozen to the channel walls. The ice thickness varies linearly symmetrically across the channel, being lowest at the center of the channel and highest at the channel walls. Ice deflections and strains in the ice cover are independent of time in the coordinate system moving with the load. The problem is solved numerically using Fourier transform along the channel and the method of normal modes across the channel. The series coefficients for normal modes are determined by truncation for the resulting infinite systems of linear algebraic equations. The ice deflections and strains in the ice plate are investigated and compared to the case of constant mean ice thickness. It is shown that even a small variation of the ice thickness significantly changes the characteristics of the hydroelastic waves in the channel.