Solution of the Problem of Oscillations of a Viscoelastic Semi-Infinite Ice Plate Using the Vertical Mode Method
УДК 517.9 + 534.1 + 532.3
Abstract
The paper considers the problem of oscillations of a semi-infinite viscoelastic plate. The viscosity of ice is modeled by the Kelvin — Voigt viscoelastic material model. The liquid is non-viscous, incompressible, and of finite depth. Oscillations of an external load placed on the free surface near the edge of the plate induce the oscillations of the plate. There is an impermeable wall on the other edge of the free surface. The solution of the problem is split into two subproblems. The first one is to find the velocity potential of the fluid flow beneath the plate, while the other one is to find the same potential beneath the free surface. The potential beneath the plate can be determined using expansion into vertical modes. Therefore, it is necessary to calculate the wave numbers of the dispersion relation considering the viscosity of ice. The potential beneath the free surface is determined using the variable separation method. Both potentials and their normal derivatives satisfy the continuity condition under the edge of the plate. The case of adding a finite floating detached plate is considered.
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References
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Copyright (c) 2025 Татьяна Андреевна Сибирякова, Кристина Евгеньевна Найденова, Константин Александрович Шишмарев
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