Abstract
Deflections and strains in an ice cover of a frozen channel caused by an underwater body moving under the ice with a constant speed along the channel are studied. The channel is of rectangular cross section, the fluid in the channel is inviscid and incompressible. The ice cover is clamped to the channel walls. The ice cover is modeled by a thin viscoelastic plate. The underwater body is modeled by a three-dimensional dipole. The intensity of the dipole is related to the speed and size of the underwater body. The problem is considered within the linear theory of hydroelasticity. For small deflections of the ice cover the velocity potential of the dipole in the channel is obtained by the method of images in leading order without account for the deflection of the ice cover. The problem of moving dipole in the channel with rigid walls provides the hydrodynamic pressure on the upper boundary of the channel, which corresponds to the ice cover. This pressure distribution does not depend on the deflection of the ice cover in the leading approximation. The deflections of the ice and strains in the ice plate are independent of time in the coordinate system moving together with the dipole. The problem is solved numerically using the Fourier transform, method of the normal modes and the truncation method for infinite systems of algebraic equations.
Highlights
The problem of the ice cover response to applied external loads has been well studied for an unbounded ice cover [1] and for a semi-infinite ice cover clamped to a vertical wall [2]
The problem of moving dipole in the channel with rigid walls provides the hydrodynamic pressure on the upper boundary of the channel, which corresponds to the ice cover
The external load is usually modelled as a point pressure or smooth localized pressure distribution moving with constant speed along the ice cover
Summary
The problem of the ice cover response to applied external loads has been well studied for an unbounded ice cover [1] and for a semi-infinite ice cover clamped to a vertical wall [2]. Small oscillations of a two-dimensional body in a liquid were studied by Sturova and Tkacheva [7, 8, 9] within the linear wave theory for finite floating ice plates. For a dipole of small intensity, the linearized Bernoulli equation is used This case corresponds to the motion of a small sphere along the channel covered with ice. The hydrodynamic loads on the ice cover caused by a moving underwater body are determined in the leading order without account for the ice deflection which is assumed small. The Kelvin–Voigt model of viscoelastic ice plate is used in the present study to estimate the strains in the ice cover In this model, hydroelastic waves decay with a distance from a load due to the damping effect. The viscoelastic ice model is closer to reality than the elastic ice plate model
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