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Article information
2019 , Volume 24, ¹ 2, p.111-128
Shishmarev K.A., Khabakhpasheva T.I.
Unsteady deflection of ice cover in a frozen channel under a moving load
The non-stationary problem of a moving external load along the surface of a frozen channel is studied in this paper. The channel has a rectangular cross section and is filled with an ideal fluid. The ice cover on the surface of the liquid is modelled by a thin elastic or viscoelastic plate (Kelvin-Voigt model), which is frozen to the channel walls. The external load is modelled by a local pressure moving at a constant speed along the channel. The ice-fluid-load system initially is at rest. The flow caused by both the moving load and the ice deflection is supposed to be potential. The problem is solved using the Fourier transform along the channel and by the method of normal modes. The presence of the channel walls and boundary conditions on them lead to an infinite (countable) number of dispersion relations and critical speeds for the hydroelastic waves propagating in the channel. Depending on the speed of the load, the form of the ice cover oscillations has one of two main cases. When the load moves at a speed lower than the first critical speed, the ice deflection is localised in the vicinity of the load. When the load is moving at supercritical speed, a system of hydroelastic waves propagating from the load is formed. The number of these wave systems is finite and depends on the relation of the speed of the load with the critical speeds for the channel. It is shown that as time increases, the solution for the ice deflection converge to a steady state in the coordinate system moving with the load. The influence of the retardation time on the formation of the ice deflections is investigated.
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Keywords: ice plate, channel hydroelastic waves, external load
doi: 10.25743/ICT.2019.24.2.010
Author(s):
Shishmarev Konstantin Alexandrovich
Position: Senior Fellow
Office: Altai State University
Address: 656049, Russia, Barnaul, Lenin Avenue 61
Phone Office: (3852) 367-067
E-mail: shishmarev.k@mail.ru
SPIN-code: 4727-2176Khabakhpasheva Tatyana Ivanovna
Dr.
Position: Senior Research Scientist
Office: Lavrentyev Institute of Hydrodynamics SB RAS
Address: 630090, Russia, Novosibirsk, Lavrentyev Avenue 15
E-mail: tana@hydro.nsc.ru
SPIN-code: 1161-4668 References:
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Bibliography link:
Shishmarev K.A., Khabakhpasheva T.I. Unsteady deflection of ice cover in a frozen channel under a moving load // Computational technologies. 2019. V. 24. ¹ 2. P. 111-128
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