For the numerical prediction of parametric roll of a tumblehome hull, captive model experiment is conducted to measure roll restoring variation in regular head seas. By utilizing measured roll restoring variation and roll damping, a 1DOF of roll model is developed. Then the Poincaré mapping method and the averaging method are applied to this model as a nonlinear dynamics approach. The comparison of steady roll amplitude and occurrence region of parametric roll between experiment and calculations shows that parametric roll of a tumblehome hull can be predicted with practical accuracy and bifurcation structures of parametric roll is also demonstrated. Lastly, the effect of bilge keels on the prevention of parametric roll is investigated.
Recently, a tumblehome vessel is under development as a new generation high-speed monohull ship. Tumblehome hull could have better propulsion and seakeeping performance than conventional hulls. However, broadside of a tumblehome hull is inclined towards inner direction, so roll restoring moment does not sufficiently increase even when she rolls. Therefore it is pointed out that a tumblehome vessel could prone to suffer stability failures in severe waves. In this research, parametric roll in head seas is experimentally and numerically investigated because it is regarded as one of the most serious scenarios for a tumblehome hull which could result in large amplitude roll motion (Bassler, 2008). To numerically predict parametric roll, captive model experiment is conducted to measure roll restoring variation in regular head seas for a tumblehome hull, which is a dominant factor of parametric roll occurrence. Parametric roll is well known as a strongly nonlinear phenomenon, thereby nonlinear dynamics approach could be useful for the prediction of parametric roll in which steady states could coexist. The Poincaré mapping method and the averaging method, which are known as geometrical and analytical approaches of nonlinear dynamics, are applied to an uncoupled roll model with measured roll restoring variation and roll damping.
