An eigenfunction expansion method (Yeung, 1981) is used to investigate the Helmholtz and higher-order symmetric resonances of the moonpool between two heaving rectangular oating bodies. It is shown that at Helmholtz resonances the hydrodynamic coefficients have distinctively bounded behavior as compared to the others modes. This serves as an identifying characteristic between the two different types of resonance modes. The parametric dependence of the heave added mass and damping coefficients on oscillation frequency, draft-to-beam ratio, and depth-to-draft ratio is illustrated and explained.


It is generally known that the free surface confined within a closed body or between two surface-piercing bodies generally exhibits resonant behavior at multiple critical frequencies. The types of resonant modes commonly encountered include a Helmholtz oscillation mode, symmetric higher-order modes and anti-symmetric or "sloshing" modes. The anti-symmetric modes are of importance in swaying and rolling motion and are probably more well known and will not be addressed here.

Because of the complex fluid-body interaction that results from such resonances, its study would be of significant interest to ship designers, who have to contend with the resulting change in ship dynamics or the reduced operational restrictions. One of the first studies in this area was performed by Wang and Wahab (1971) who studied the moonpool between two semi-circular bodies. They identified the presence of the "zeroth" mode which we now know to be the Helmholtz mode. An interesting asymptotic analysis was used by Marthinsen and Vinje (1985) to obtain the study Helmholtz resonance in infinite-depth water. Their results had some nonlinear features in the gap, but the far field is linear. Other studies involving the Helmholtz mode include Miles (1974), Miles and Lee (1975) and Ünlüata and Mei (1975), in the context of harbor resonances.

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