Stability of Ice Cover Oscillations in a Channel Problem Solution with Initial Data
Abstract
In this paper, an initial-boundary problem of ice cover oscillations in an infinite channel caused by a moving load is considered within the linear theory of hydroelasticity. Mathematical model is based on a combined system of differential equations describing vertical deflection of the ice cover and motion of fluid in the channel. The ice cover is modeled by the equation of a thin viscoelastic plate. Viscoelastic properties of ice are modeled by the Kelvin-Voigt rheological law. The liquid in the channel is inviscid and incompressible. The relation between the viscoelastic and hydrodynamic parts of the problem is established by the linearized kinematic and dynamical conditions. The system of equations is closed by conditions of clamped edges for the plate on the walls of the channel, conditions of impermeability for the flow velocity potential, and damping conditions for the oscillations far away from the load. The investigation in this paper is devoted to the correctness of problems formulations described by combined equations of a viscoelastic plate and an ideal fluid. In section 1, the stability theorem for the classical solution of the initial boundary-value problem of viscoelastic oscillations of the ice cover in the channel with respect to initial data is proved. In section 2, the similar theorem is proved for elastic oscillations of the ice cover. Theorems are proved using energy estimation methods and special functional inequalities. Stability of described problems is studied for finite times.
DOI 10.14258/izvasu(2017)4-30
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