On natural frequencies of three-dimensional moonpool of vessels in the fixed and free-floating conditions

The hydrodynamic interactions between the vessel motion and resonant wave response inside the three-dimensional moonpool are studied in the present paper. In particular, the shift of natural frequencies of a three-dimensional moonpool in the fixed and free-floating conditions is computed and examined systematically. Barges with different moonpool dimensions are analyzed to examine how the moonpool configurations affect the shift of resonant frequencies. Detailed analyses are performed for cases with and without recess. Numerical computations are performed for regular waves with wave headings theta = 0 degrees, 45 degrees and 90 degrees. Free-surface elevations inside the moonpool with respect to the incident wave frequencies are computed for both fixed and free-floating conditions. It is observed that natural frequencies of the moonpool in the free-floating condition are higher than those in the fixed condition. For cases without recess, the shift of resonant frequency is more prominent in piston mode resonance, in particular for shallow or long moonpools. In contrast, for cases with a recess, the shift of resonant frequency in the first sloshing mode is relatively larger than that in piston mode. In addition, the effects of motion RAOs on the free-surface elevation inside the moonpool in the free-floating condition are also examined. It is found that the moonpool resonance can induce a local hump in heave and pitch responses. Moreover, through deriving a modified frozen mode approximation model, we reveal that, comparing to the fixed condition, the vessel motion in the free-floating condition yields a reduction in the added mass due to the fluid underneath the moonpool so that the piston mode resonant frequency increases.