Numerical prediction on parametric roll resonance for a ship having no significant wave-induced change in hydrostatically-obtained metacentric height

Abstract

Parametric roll resonance is known as one of dangerous modes of ship motions in waves. This resonance occurs as a result of restoring variation in astern or head seas. This paper focuses on the parametric resonance observed in head seas for a model of an Icelandic trawler that has no distinct wave-induced change in her metacentric height, which is hydrostatically calculated. Two mathematical models, a 1 degree-of-freedom (DOF) model with balanced heave and pitch motions and a 6 DOF model were used to explain the parametric roll resonance of the ship in head waves. Both the mathematical models take the change of the righting arm into account; the 1 DOF model assumes static balance in heave and pitch, while the 6 DOF one takes coupling between roll and vertical motions taken into account. Only the 6 DOF model, however, successfully reproduced the occurrence of parametric rolling of the ship. This suggests that coupling effect from heave and pitch to roll restoring is essential for parametric rolling in head seas. Furthermore, numerical simulation based on the 6 DOF model shows parametric rolling does not depend on small change in heading angle very much but is sensitive to the relationship between the natural pitch period and the natural roll period.