Identification of two roll resonant periods of ship motion coupling with liquid sloshing inside

Existing studies showed that the roll motion response of ships fitted with sloshing tanks is typically characterized by two peaks and a trough over a range of incident wave frequencies. There has not been a convincing physical interpretation of the observed behavior. The present study, through a conceptual model of the coupled system and a series of physical and numerical tests, reveals that the two-peak responses occur at the first and second resonant frequencies of the system and that the trough response appears at the natural frequency of internal sloshing. The motions of the ship and sloshing liquid at the resonant frequencies constitute two normal modes of the system: in-phase and out-of-phase. While the resonant frequency corresponding to the in-phase mode can readily be determined through a free decay test experimentally, the determination of the resonant frequency associated with the out-of-phase mode is not straightforward. To this end, a numerical approach is proposed to determine the resonant frequency associated with the out-of-phase mode.