On The Problem of the Viscous Broken Ice Response to a Load Moving Along a Channel
УДК 517:551.3
Abstract
The problem of the broken ice response to a moving external load in a channel is considered.
The review of the well-known results is presented in paragraph 1.
The formulation of the problem is given in paragraph 2. The channel has a rectangular cross section with finite depth and width. The fluid in the channel is ideal and covered with broken ice. The broken ice is modeled by a thin elastic plate with zero rigidity. The external load is modeled by a smooth localized pressure and moves along the upper surface of the broken ice at a constant speed. The case taking into account the viscosity of broken ice is considered. The flow caused by the deflection ofthe broken ice is potential. The broken ice deflection and the potential of the flow satisfy the damping condition at a distance from the load.
The method of the solution is described in paragraph 3. The solution is sought in the form of a traveling wave in a coordinate system moving together with the load. The problem is solved using the Fourier transform along the channel and the method of separation of variables. The solution is obtained in the form of integrals from the Fourier image of the deflection of the broken ice. These integrals are solved numerically for some given parameters of the problem.
The results are discussed in conclusion.
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References
Squire V., Hosking R., Kerr A., Langhorne P. Moving loads on ice. Kluwer Academic Publishers, 1996.
Shishmarev K., Khabakhpasheva T., Korobkin A. The response of ice cover to a load moving along a frozen channel. Applied Ocean Research. 2016. Т. 59.
Kozin V.M. Resonance Method of Breaking of Ice Cover. Inventions and Experiments. Akad. Estestvoznaniya, M., 2007.
Schulkes R., Sneyd A. Time-dependent response of floating ice to a steadily moving load // Journal of Fluid Mechanics. 1988. 186.
Korobkin A., Khabakhpasheva T. Plane problem of asymmetrical wave impact on an elastic plate // Journal of Applied Mechanics and Technical Physics. 1998.
Khabakhpasheva T. Impact of a surface wave on an elastic hull. Fluid Dynamics. 2006.
Коробкин А.А., Папин А.А., Шишмарев К.А. Аналитическое и численное исследование квазиизотермической задачи взаимодействия ледового покрова канала и поверхностных волн // Известия АлтГУ 2012. Вып. 1/2 (73).
Коробкин А.А., Папин А.А., Шишмарев К.А. Поведение ледового покрова канала под действием поверхностных волн // Известия АлтГУ 2012. Вып. 1/1 (73).
Korobkin A., Khabakhpasheva T., Papin A. Waves propagating along a channel with ice cover // European Journal of Mechanics B/Fluids. 2014. V. 47.
Batyaev E.A, Khabakhpasheva T.I. Hydroelastic waves in channel with free ice cover. Fluid Dynamics. 2015, № 6.
Zhestkaya V.D. Numerical solution of the problem of an ice sheet under a moving load // Journal of Applid Mechanics and Technical Physics, 1999, V. 40(4).
Жесткая В.Д., Козин В.М. Численное решение задачи о воздействии ударного импульса на ледяной покров // ПМТФ. 2008. Т. 49. № 2.
Brocklehurst P. Hydroelastic waves and their interaction with fixed structures // PhD thesis, University of East Anglia, UK. 2012.
Sturova I.V., Tkacheva L.A. Wave motion in a fluid under and inhomogeneous ice cover // Journal of Physics: Conference Series. 2017. V. 894. № 1.
Стурова И.В., Ткачева Л.А. Колебания ограниченного ледяного покрова при локальном динамическом воздействии // Полярная механика. 2016. № 3.
Ткачева Л.А. Колебания ледяного покрова с трещиной при воздействии периодической по времени нагрузки // Известия РАН. Механика жидкости и газа. 2017. № 2.
Tkacheva L.A. Vibrations of an ice sheet with crack under a time-periodic load // Fluid Dynamics. 2017. V. 52. № 2.
Токарева М.А. Конечное время стабилизации решения уравнений фильтрации жидкости в пороупругой среде. // Известия Алт. гос. ун-та. 2015. Т. 2. № 1.
Tokareva M.A. Solvability of initial boundary value problem for the equations of filtration in poroelastic media // Journal of Physics: Conference Series. 2016. V. 722. № 1.
Kozin V.M., Zhestkaya V.D., Pogorelova A.V., Chizhumov S.D., Dzhabailov M.P, Morozov VS., Kustov A.N. Applied problems of the dynamics of ice cover. M., 2008.
Шишмарев К.А., Завьялова К.Н. Свободные и вынужденные волкы в канале, покрытом битым льдом // МАК: Математики — Алтайскому краю : cборник трудов всерос. конфер. по математике. 2017.
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