The three-dimensional problem of the coupled time-harmonic motion of a freely floating body and water covered by brash ice

Abstract

A mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium is considered. The water occupies a half-space into which a surface-piercing body is immersed, thus allowing us to study the coupled motion which is assumed to be of small amplitude. The corresponding linear setting for time-harmonic oscillations reduces to a spectral problem whose parameter is the frequency. A constant that characterises the brash ice divides the set of frequencies into two subsets and the results obtained for each of these subsets are essentially different. For every frequency from a finite interval adjacent to zero, a family of motionless axisymmetric bodies trapping waves is constructed by virtue of the semi-inverse procedure. For sufficiently large frequencies outside of this interval, all solutions of finite energy are trivial.