Sway Added Mass of a Rectangular Cylinder in a Restricted Water

TLDR: In this paper, the authors considered the sway added mass of a rectangular cylinder in a restricted water by applying Hamilton's principle as the frequency tends to zero and derived an approximate formula for the cases of the cylinder swaying at the center of a narrow or wide canal relative to a cylinder, at off-center location in a canal, and in the restricted water with a single wall.

Abstract: In this paper, the sway added mass of a rectangular cylinder in a restricted water is considered by applying Hamilton's principle as the frequency tends to zero. The present method is an extension of Isshiki's method proposed in 1978. In the present method, it is assumed that the fluid velocity distribution in each subdomain of the fluid can be represented by higher order polynomials while Isshiki assumed linear velocity distribution. The fluid flow is assumed as a rotational motion in the present analysis. However, the results obtained from the present method show good agreement with Bai's numerical results for the case of large clearances between a canal wall and a cylinder. From Kelvin's minimum energy theorem, we can see that the value of sway added mass obtained from the present method approaches the upper bound. The approximate formula obtained in the present study takes a simple form which consists of the dimensions of the canal and the cylinder. The present formulae are derived for the cases of a rectangular cylinder swaying at the center of a narrow or wide canal relative to a cylinder, at off-center location in a canal, and in the restricted water with a single wall. From the results of numerical calculation, it is concluded that the sway added mass in restricted waters is more affected by water depth than clearance between a wall and a cylinder.