Resonant response of a moonpool with a recess

Resonant modes of motion are analyzed in a moonpool with a recess, of the same type studied by Guo et al. [1], [2] and Molin [3]. The length and depth of the recess are varied, as in [3]. The moonpool is placed within a rectangular barge, which has dimensions similar to the drillship in [1], [2]. The complete structure consisting of the barge and moonpool is analyzed by solving the diffraction problem with incident waves, and the resonant frequencies are found which maximize the free-surface elevation in the moonpool. The resonant frequencies are also identified with singularities in the surge and heave added-mass coefficients. These results are compared with different approximations, which may be useful for estimating the resonant frequencies. In the simplest approximation the resonant frequencies of sloshing modes are determined from the wavelengths of standing waves in a closed basin with the same length as the moonpool. More rational and complete approximations are developed similar to those in [3], with the moonpool and exterior fluid domain analyzed separately and the solutions matched at the interface. This leads to a linear system of equations involving generalized added-mass coefficients in the two domains. Analytical and numerical methods are described for the evaluation of these coefficients.