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Waves and moving loads along frozen channels

Presented by: 
Tatiana Khabakhpasheva
Thursday 5th October 2017 - 11:45 to 12:30
INI Seminar Room 1
Co-authors: Shishmarev Konstantin (Altay State University, Barnaul, Russia), Korobkin Alexander (University of East Anglia, Norwich, UK)

Hydroelastic waves caused by external loads are well studied for an ice cover of infinite extent. Similar problems, but with an ice cover clamped to the vertical walls in a channel, are studied in less detail. However, the presence of the walls and clamped conditions of the ice to the walls may significantly affect distributions of deflections and stresses in the ice cover. These problems are of practical importance because laboratory experiments on loads moving along an ice cover are performed in ice tanks. The response of the ice cover caused by a moving localized external load is studied numerically and analytically for a channel with rectangular cross section. The equation of viscoelastic thin plate with a given damping coefficient is used for describing oscilations of the ice. The liquid beneath the ice is inviscid and incompressible, the flow is potential. The problem is solved with the help of the Fourier transform along the channel and the method of normal modes across the channel. The numerical results show a significant difference in the distributions of the ice deflections in the channel and in the ice cover of infinite extent for the same loading conditions. For the ice cover of infinite extent there is a single dispersion curve and two critical velocity of hydroelastic wave propagation, whereas the presence of the channel walls leads to the infinite number of the dispersion curves and critical speeds. The critical speeds depend on the channel width and decrease with increase of the distance between the walls of the channel.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons