Method for solving the problem of load movement over the ice cover of a reservoir along a complex trajectory

Introduction. The development of the polar regions of the World Ocean contributed to an increased interest in studying wave processes in water bodies with ice cover caused by the action of a mobile load. In most papers of domestic and foreign scientists, the ice sheet was considered as an elastic or viscoelastic plate loaded with a rectilinearly moving vertical force. However, when modeling the impact of vehicles on the ice cover, it is of interest to investigate problems in which the force moves along a more complex trajectory. Therefore, this study aims at developing a method for studying the behavior of the ice cover under the action of a force moving along a trajectory of a complex shape, obeying an arbitrary law of motion.Materials and Methods. A method for solving problems of the action of an arbitrarily moving force on the ice cover of a reservoir of finite depth filled with an inviscid incompressible fluid is proposed. The ice cover was considered as a viscoelastic plate lying on the surface of a liquid in a state of potential flow. A concentrated force moving along an arbitrary closed trajectory and being periodic in time was applied to the upper surface of the plate. Hydrodynamic pressure acted on the lower surface of the plate from the liquid side. Due to the periodicity of the load applied to the plate, an integral time transformation was used to solve differential equations describing the behavior of this system. Further, using traditional methods, formulas were obtained for calculating stresses and displacements in the plate and components of the velocity vector of liquid particles. These formulas were presented in the form of an iterated integral. Numerical methods were used to calculate integrals.Results. Calculations showed that the deflection of the ice cover increased markedly with the growth of speed and tangential acceleration of the load movement. An increase in the relaxation time of ice and a decrease in the radius of the trajectory of the load also caused an increase in deflection. The distribution of the fluid particle velocity vector over the depth of the reservoir was calculated.Discussion and Conclusions. The proposed method has shown its efficiency in solving problems about the impact of a moving load on the ice cover of a reservoir. With its help, the influence of the curvature of the trajectory of motion and the mechanical properties of ice, the kinematic characteristics of the movement of the load on the deflection of the ice cover was investigated. The method simulates the impact of vehicles on the ice cover of a reservoir. The results of its application can be used under the construction of ice roads or airdromes on ice.