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A mechanical system consisting of water covered by brash ice and a bodyfreely floating near equilibrium is considered. The water occupies a half-spaceinto which an infinitely long surface-piercing cylinder is immersed, thusallowing us to study two-dimensional modes of the coupled motion which isassumed to be of small amplitude. The corresponding linear setting fortime-harmonic oscillations reduces to a spectral problem whose parameter is thefrequency. A constant that characterises the brash ice divides the set offrequencies into two subsets and the results obtained for each of these subsetsare essentially different.  For frequencies belonging to a finite interval adjacent to zero, the totalenergy of motion is finite and the equipartition of energy holds for the wholesystem. For every frequency from this interval, a family of motionless bodiestrapping waves is constructed by virtue of the semi-inverse procedure. Forsufficiently large frequencies outside of this interval, all solutions offinite energy are trivial.

On freely floating bodies trapping time-harmonic waves in water covered by brash ice