Study On Forcedly-parametrically Excited Rolling Of A Ship In Oblique Seas

When a ship is sailing in oblique seas, parametric excitation and forced excitation will act on the ship at the same time, and the ship will encounter forcedly-parametrically excited rolling, which lead to large rolling or even capsizing. This paper aims at exploring mechanical mechanism of forcedly-parametrically excited rolling of the C11container ship in oblique seas, which is of great importance to guide ships to navigate safely in severe seas. Main contents are as follows:Because heave and pitch have a large influence on roll of the ship sailing in waves,3-DOF (three degrees of freedom) motion equations of roll, heave and pitch are established, considering nonlinear restoring forces and nonlinear roll damping. Roll restoring moment varying with time is parametric excitation, and instantaneous nonlinear restoring force are programmed, according to the instantaneous relative position of the ship and waves. The form of roll nonlinear damping contains linear term and cubic term, and damping coefficients are obtained by experiment. The added mass coefficient, damping coefficients of heave and pitch, and wave forced excitation are calculated by three-dimensional potential flow theory. Differential equations of the ship motions are solved by using the Runge-Kutta method, and analyze the effects of related factors.Meanwhile, a simple method to forecast rolling motion in oblique seas is proposed. Considering the influents of harmonic heave and pitch, and initial wave crest positions, initial metacentric height based on procedures of instantaneous nonlinear restoring force is calculated. And then1.5-DOF roll motion equations are established and solved by using the Runge-Kutta method.Numerical analysis found that initial metacentric height is a single frequency harmonic variation, when the ship roll motion is large. Initial metacentric height can be fitted to the harmonic function and got into the differential equations. Approximate analytical solutions are obtained by using multiple scales method, and stability of rolling is analyzed according to Floquet theory, determining parameter ranges of the ship forcedly-parametrically excited rolling.Studies show:forcedly-parametrically excited rolling is multi-frequency response, including wave excitation frequency and primary parametric resonance frequency. At the case of meeting conditions of parametric rolling, forcedly-parametrically excited rolling may disappear with changing initial wave crest position. For C11container ship, the ship may easily encounter forcedly-parametrically excited rolling in bow oblique seas, which is more dangerous than in stern oblique seas. Meanwhile, with the increasing of the wave height, the ranges of wave length, speed and heading angle leading to forcedly-parametrically excited rolling are also expanded.Through the figure of stability region, the ranges of wave height, and the ratio of encounter frequency and roll natural frequency are determined, when forcedly-parametrically excited rolling of the ship occurs in oblique sea. Moreover, as the increase of wave height, the range of the ratio of encounter frequency and roll natural frequency is expanded, but when wave height continues to increase, the range of the ratio tends to decrease. Through bifurcation diagrams of roll varying with encounter frequency, the range of encounter frequency occurring forcedly-parametrically excited rolling is determined. When main resonance of ship rolling occurs, roll motion is a single periodic motion, and when primary parametric resonance occurs, roll motion is a twice periodic motion.