Simulation of oscillations in an infinite floating ice plate

Background. In a cold climate is always an urgent problem of operation of the ice cover. The paper proposes an analytical method for solving the problem of oscillations of a free-floating infinite ice plate in contact with water as a thin plate on an elastic base, for the study of which the methods of the theory of thin shells and plates are applicable. Material and methods. The method is based on generalized discrete Fourier transform. The solution is obtained in the class of almost-periodic functions (Bohr-Fourier series). Results. The amplitude function of oscillations of an arbitrary thin plate on an elastic base and an infinite ice plate in contact with water in the form of Bohr - Fourier series is constructed. The belonging of the required functions to the class of almost-periodic functions is shown. A numerical example describing the oscillations of an ice plate is considered. Graphs of the deflection of the median plane of the plate at the specified moments of time are constructed. Conclusions. The analytical solution of such problems in the form of Bohr - Fourier series with functional coefficients greatly simplifies the solution process and makes the further process of solving and graphical representation quite simple.