On the Hydrodynamic Forces of Oscillating Cylinders in the Presence of a Free Surface

The integral equation method to solve the boundary-value problem of a 2-dimensional body oscillating in the presence of a free surface generally breaks down at and near irregular frequencies due to the hypothetical flow inside the body. In this paper singularity distributions were extended to an inner free surface to remove the irregular frequency as Ohmatsu's work in 1978, and the solution for the above problem was found by using stream function. For various bodies including Lewis form cylinders, the hydrodynamic forces were calculated numerically at various wave numbers. From the results we concluded that the irregular frequencies can be removed even for the Lewis form cylinder as Ohmatsu done for circular cylinders, and calculated hydrodynamic forces by the present method are little higher than those of Ohmatsu's when the singularities are put on the inner free surface of the body. We specially point out that the solution for heaving motion converges in an oscillatory manner but not for swaying and rolling motions.