Numerical Simulation Of Parametric Rolling Based On A Weak Nonlinear Model

Since ancient times,there are many phenomena in the practice of ship navigation which cannot be explained by linear theory,and the parametric rolling is one of them.With the development of large-scale container ship,parametric rolling has become one of the failure modes to be evaluated in the process of ship design.In this paper,the direct calculation method of parametric rolling is studied in the following four aspects.First,a weak nonlinear six-DOF motion model is established.Firstly,based on the theory of potential flow and the theory of rigid body dynamics,the differential equations of six-DOF for the movement of ships in waves are established,and then the linear recovery force and incident force in the equation are modified to be the result of the instantaneous wet surface integral along the ship,which is determined by the incident wave surface and the instantaneous attitude of the ship.The linear roll damping moment is corrected to a more precise form.In this way,a weak nonlinear motion model of six-DOF is obtained.Secondly,the weak nonlinear three-DOF motion model is established and solved.The six-DOF model is simplified into the three-DOF model of heave-roll-pitch,and the motion time history of C11 container ship in longitudinal wave and oblique wave is calculated by this model,and compared with the model test results,the accuracy of the model is verified.Then,the model is used to forecast the parametric rolling phenomenon of 20,000 TEU container ships.Thirdly,a one-DOF roll motion model is established and solved.Based on the idea of 1.5-DOF model,the three-DOF model is further simplified,a new method considering heave and pitch coupling items is proposed,and an expression of fitting righting arm is proposed.Using this expression,three kinds of 1.5-DOF models are calculated,and the accuracy of the expression is verified.The above expression,combined with the new method of heave and pitch coupling,can provide a more accurate mathematical model of one-DOF for the analytic analysis of parametric rolling in regular wave and the probability analysis of parametric rolling in irregular wave.Finally,a unified model of maneuvering and seakeeping motion is proposed.Based on the principle that the high and low frequency motion of the ship when sailing in the wave can be separated,the weak nonlinear motion model in the wave is combined with the ship maneuvering equation in the static water,and a unified model ofmaneuvering and seakeeping motion is proposed,and the model of C11 container ship is calculated by using it.The model takes into account the influence of yaw and rudder force,and is suitable for more accurate prediction of the parametric rolling phenomenon of ship in actual navigation,especially in oblique wave.