An analytical solution of the problem of deflection of the ice cover of varying thickness is obtained using the Fourier and Laplace transforms and the asymptotic expansions. The influence of varying thickness on the ice cover deflections during load movement is analyzed.
There are number of papers devoted to behavior of floating ice cover influenced various types of dynamic load. The works of Kheisin (1967) and Squire et al (1996) are fundamental in this field. Usually the ice cover is modeled as elastic or visco-elastic plate with constant thickness. However, ice is not isotropic in real conditions. An example of ice thickness profile is presented in Squire et al (2009). Since the problem of behavior of the ice cover varying thickness subjected to a load is insufficiently understood, there is a need to develop mathematical apparatus for solving this problem. Safety exploitation of the ice as ice roads and crossing requires consideration of many factors, including variability of the ice thickness.
Investigations of the propagation of waves in the ice cover of variable thickness are presented in the works Porter and Porter (2004a), (2004b), Bennetts et al. (2007a), Vaughan and Squire (2006). Porter and Porter (2004a) considered the problem of wave propagation in a floating ice plate of variable thickness with the influence of bottom topography solved in three-dimensional statement using Rayleigh-Ritz method. An alternative method for solving similar problem is proposed in the work of Bennetts et al. (2007a). In the work of Vaughan and Squire (2006) the two-dimensional model describing the process of propagation of waves under the ice cover containing the region of variable thickness is presented. Axisymmetric problem of scattering incident waves round ice floe floating on the liquid of constant depth considered in the work of Bennetts et al. (2009).