Mathematical modelling of antirolling tanks and their application in the case of parametric resonance

The present paper describes the development of a mathematical model in which the fluid motion inside a U tank is non-linearly coupled to the heave, roll and pitch motions of the ship. The main purpose of the investigation is centred on the control of roll motion in the case of parametric resonance in longitudinal waves. A transom stern small vessel, a vessel well known to be quite prone to parametric amplification is employed in the study. The results are presented in the form of limits of stability, with encounter frequency and wave amplitudes as parameters. Distinct dynamical characteristics are discussed and conclusions are drawn on the relevant parameters for the efficient control of the roll amplifications in head seas.