Action of Periodic Surface Pressure on an Ice Cover in the Vicinity of a Vertical Wall
I. V. Sturova
Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: линейная теория мелкой воды, изгибно-гравитационные волны, вязкоупругий ледяной покров, вертикальная стенка, периодическая внешняя нагрузка, краевые волны, linear shallow water theory, bending gravity waves, viscoelastic ice cover, vertical wall, periodic external load, edge waves
Abstract
This paper presents the solution of the linear hydroelastic problem of stabilized forced vibrations of a semi-infinite ice cover under the effect of localized external load. The ice cover is simulated by a viscoelastic thin plate, the thickness of the liquid layer is assumed to be small, and the shallow water theory is used. The liquid is limited by a solid vertical wall, and the straight edge of the elastic plate adjacent to the wall can be both free and clamped. The solution is obtained with the help of the Fourier integral transform. The behavior of the ice cover is studied in terms of the frequency of the external load and boundary conditions on the edge of the plate. It is shown that, in the case of a free edge of the plate, there are considerable bends on the edge, which could be comparable with bends at the center of the pressure impact region. It is established that, due to the existence of wave movements of the type of edge waves, the external load energy is transferred to larger distances along the free edge, and there are significant bending moments on the edge of the clamped plate, which can lead to fracture of the ice cover at sufficiently great intensity of the external load.
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