LOW-FREQUENCY OSCILLATIONS OF A PARTIALLY SUBMERGED CYLINDER OF ARBITRARY SHAPE

This paper is concerned with the low-frequency asymptotic solution of the deep-water radiation problem for a partially submerged cylinder of arbitrary (nonsymmetric, non-smooth) shape. A five-term asymptotic ex pansion of the wave potential is derived which reduces to a three-term expansion when the mean volume flux across the wetted surface of the cylinder vanishes. The former case corresponds to the heaving motion a nd the latter one to the swaying or rolling motions of a floating cyli nder. This expansion is then used to obtain explicit low-frequency asy mptotic expansions for all elements of the added-mass and damping tens ors, as well as the amplitude and the phase angle of the outgoing wave s at infinity. Most of the terms in these expansions are given in term s of simple geometric characteristics (beam, area, and centroid's posi tion) of the immersed part of the cylinder, as well as the formal-limi t (omega = 0) added mass. Numerical comparison between the asymptotic results and the ''exact'' ones, obtained by solving numerically the fr equency-dependent problem, show that the agreement is satisfactory in the range 0 < omega < 0.5 and, in some cases (e.g., for lateral motion s), in 0 < omega < 0.6, where omega is the nondimensional frequency no rmalized by the beam of the cylinder. (Note that the whole range of in terest, up to the high-frequency limit, is about 0 < omega < 2.0.)