Analytical calculation of hydrodynamic coefficients of an oscillating horizontal circular cylinder using the bi-polar coordinate

The added mass and wave damping of an oscillating horizontal circular cylinder are analytically calculated using the bi-polar coordinate. In the bi-polar coordinate, a point is uniquely defined by two orthogonal circles. These circles can be used to represent the mean surface of a partially- and a fully submerged oscillating circular cylinder along with the mean position of the free surface. By expressing boundary conditions on the surface of the cylinder and the free surface in terms of the bi-polar coordinate, the Laplace equation in terms of the velocity potential is analytically solved, and, thus, the added mass and wave damping are analytically obtained. Both partially/fully submerged and heave/surge cases are considered. The analytical results are compared with existing numerical studies using the boundary element method. They agree with each other very well.