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Using the multipoles method, we formulate the problems of water wave radiation (both heave and surge) by a submerged circular cylinder in water with an ice-cover, the ice-cover being modelled as an elastic plate of very small thickness. This leads to an infinite system of linear equations which are solved numerically by standard techniques. The added- mass and damping coefficients for a heaving and surge problems are obtained and depicted graphically against the wave number for various values of flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity and surface density of ice-cover are taken to be zero, the ice-cover tends to free-surface then the curves for added-mass and damping coefficients exactly coincide with the curves for the case of water with free surface. Also it is observed that the added-mass and damping coefficients for the two modes of motion are here also the same.
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Das et al. (2019) studied this question.
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