Exciting forces for a pair of coaxial hollow cylinder and bottom-mounted cylinder in water of finite depth

Abstract

We consider two coaxial vertical geometrical shapes in the form of a riding hollow cylinder and a bottom-mounted solid cylinder, the latter being an approximation for a caisson. The present problem of diffraction by these two cylinders can be considered as a wave energy device. The energy that is created and transferred finds its use in a number of practical applications. We use the method of separation of variables to obtain the analytical expressions for the diffracted potentials in clearly identified regions. By using the appropriate matching conditions along the virtual boundaries between the regions, we deduce and solve a system of linear equations in the unknown coefficients. The analytical expressions of the potentials allow us to obtain the exciting forces acting on both the cylinders. A set of exciting forces are obtained for different radii of the cylinders and for different gaps between the cylinders. It is observed that changes in radius and the gap have significant effect on the forces. These results are depicted graphically and compared with available results. It is found that the exciting forces are of consequence only at lower frequencies.