Hydroelastic wave diffraction by a vertical circular cylinder standing in a channel with an ice cover

Abstract

The problem of hydroelastic wave diffraction by a surface-piercing vertical circular cylinder mounted on the bottom of an ice-covered channel is considered. The ice sheet is modelled as an elastic thin plate with homogeneous properties, while the linearized velocity potential theory is adopted to describe the motion of the fluid. The solution starts from the Green function satisfying all other boundary conditions apart from that on the body surface. This is obtained through applying a Fourier transform in the longitudinal direction of the channel and adopting an eigenfunction expansion in the vertical direction. The boundary conditions on the side walls and ice edges are imposed through an orthogonal product. Through the Green function, the velocity potential due to a surface-piercing structure with arbitrary shape can be expressed through a source distribution formula derived in this work, in which only integrals over the body surface and its interaction line with the ice sheet need to be retained. For a vertical circular cylinder, the unknown source distribution can be expanded further into a Fourier series in the circumferential direction, and then the analytical solution of the velocity potential can be obtained further. Extensive results and discussions are provided for the hydrodynamic forces and vertical shear forces on the cylinder, as well as the deflection and strain of the ice sheet. In particular, the behaviour of the solution near one of the natural frequencies of the channel is investigated in detail.