The radiation of small-amplitude waves by an oscillating, horizontally-submerged disk of elliptic cross-section located at a finite depth beneath the free-surface is investigated analytically. The theoretical formulation leads to solutions for the fluid velocity potential in terms of series of Mathieu and modified Mathieu functions of real argument. Numerical results are presented for the added-mass and radiation damping coefficients of the disk in the various oscillation modes for a range of wave and structural parameters.
Recently, Zhang and Williams(1995), presented a theoretical solution to the problem of wave scattering by a disk of elliptic cross section horizontally submerged at a finite depth beneath the free surface, using an eigen function expansion approach. They presented numerical results for the wave-induced force and moments and the water surface elevation in the vicinity of the disk for a range of wave and geometric parameters. Their analysis clearly showed the effect of wave focusing around the rear of the disk. In the present paper, a similar analytical approach will be utilized to study the corresponding problem of the radiation of small-amplitude waves by an oscillating, horizontally-submerged disk of elliptic cross-section. The elliptic geometry allows consideration of the effects of wave direction and aspect ratio on the wave scattering characteristics of the body. Later Williams (1985a) presented two approximate solutions to the scattering problem, one based on an expansion of the exact solution of Chen and Mei for small values of the elliptic eccentricity, the other based on an integral equation technique involving the application of Green's theorem. Both methods showed excellent agreement with the exact solution and a considerable saving in computational effort was reported. Chen and Mei (1973) also investigated the hydrodynamic loading on a stationary platform of elliptical shape partially immersed in the free-surface.