Numerical calculation and mechanical mechanism analysis of ship parametric rolling

ZHU Jun*1，ZHU Tao2，WANG Zhiyu1，XIA Qiqiang2，HUANG Kunlun1，GE Yijun1 1 College of Naval Architecture and Ocean Engineering，Naval University of Engineering，Wuhan 430033，China 2 Institute of Specialized Services，Naval Research Academy，Shanghai 200235，China parametric rolling is a special instability phenomenon of ship in the wave. The current research proves that the change of the stability parameter when the wave passes through the hull is the reason for the rolling motion of the hull，but the mechanical mechanism is unclear. Firstly，based on the equations of heave and pitch coupled motion in inertial coordinates and the equations of roll motion in hull coordinates，a hybrid dynamic model of heave pitch and roll was established； secondly，the proposed method of oscillating strip method was used to calculate the motion of ship parametric rolling numerically，and a criterion for parameter roll was proposed based on the principle of energy. The research results show that the mechanical mechanism for the occurrence of parametric rolling of a ship is that the energy absorbed by the recovery moment coefficient during the increase of the roll angle is less than the energy released by the recovery moment during the decrease of the roll angle；the criterion is that the phase angle of the first-order harmonic component of the recovery torque coefficient lies within［0, Defining the mechanical mechanism of parametric roll is helpful to understand the physical nature of the parametric roll instability mode. The proposed parametric roll criterion is of reference significance for the development of the second generation intact stability criterion of the ship.

Abstract：［Objective］The ［Results］

π］.［Conclusions］ words：ship；waves；parametric Key ［Methods］

rolling；mechanical mechanism