Hydroelastic wave interaction with a circular crack of an ice-cover in a channel

Hydroelastic wave interaction with a circular crack of an ice-cover in a channel together with some related problems is considered, based on the linearized velocity potential theory and Kirchhoff plate theory. The domain decomposition method is adopted in the solution procedure. Two sub-domains are divided by the crack, one below the inner ice sheet and the other below the outer ice sheet. By using the Green function of an ice-covered channel, the velocity potential in the outer domain is established from the source distribution formula over an artificial vertical surface extended from the crack. The source distribution is expanded in both vertical and circumferential directions, which allows the velocity potential to be obtained in an explicit form with unknown coefficients. The velocity potential in the inner domain is expanded into a double series. An orthogonal inner product is used to impose continuity conditions on the artificial vertical surface and the edge conditions at the crack. The derived formulation is not just limited to the circular crack problem but can also be readily used in a variety of other problems, including wave diffraction by a surface-piercing vertical cylinder, polynya and circular disc floating on the free surface in a channel. Extensive results are provided for the forces on the inner ice sheet, the transmission and reflection coefficients. In particular, a detailed analysis is made on their behaviours near the natural frequencies of the channel, and the natural frequencies corresponding to the motion of the inner ice sheet.