Problem Formulation of Ice Plate Viscoelastic Oscillations in a Channel Caused by a Moving Load
In this paper, hydroelastic waves in an icecovered channel that are generated by a load moving along an ice sheet are studied. The external load is modeled by a localized smooth pressure distribution. A mathematical model is based on the differential equation of viscoelastic ice plate oscillations and the Laplace equation for the velocity potential of fluid flow under the ice sheet. These equations are supplemented by boundary conditions of impermeability of channel walls and channel bottom, conditions of ice rigid fixing on the channel walls, and kinematic and dynamic conditions at the interface between ice and liquid. The travelling wave solution, which is time-independent in a coordinate system moving with the external load, is studied. The Fourier transform along the channel is utilized to reduce the problem under consideration to a twodimensional problem of wave profile across the channel, which is solved by the fixed beam normal modes method. The paper consists of 2 parts. In the first part, the ice defection and strains in the ice sheet in the channel are calculated for given ice characteristics. The numerical results are analyzed and discussed.
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