Study On The Nonlinear Rolling And Capsizing Mechanism Of Ship In Random Longitudinal Wave

The parametrically excited roll motion of ship in following waves can aroseunstable rolling, which is the main cause of ship capsizing. The dynamiccharacteristics of roll motion due to parametrical excitation are investigated, the goalis to reveal the capsizing mechanisms of ship in the longitudinal waves due toparametrical excitation.The method of estimating the non-linear damping coefficients is proposed by theenergy principal based on the free rolling curves. A principal advantage of thistechnique is that, the damping model need not to be known, and that, because thenon-linearity in the restoring moment can be properly accounted for, it is not limitedto small angles of roll. The express formulas of linear-plus-cubic and linear-plus-quadratic damping models are examined, and the calculated results from differentexpress formulas of damping are compared to the experimental data. According to thedata of free decay experiment of the model of 15000 tons container ship, thenon-linear roll damping coefficients are obtained.The differential equation of ship's parametrically excited roll motion isestablished considering the metacentric height GM-variation due to the pitch, heaveand motions of the longitudinal waves. The metacentric height is regarded as arandom parametrical excitation. The function of the variation between the metacentricheight in wave and in still water around the mean draft is resolved, with respect to theexcited wave, pitch motion, heave motion, and hull geometry of the container ship of150 meters long and 27 meters wide. The random waves with significant wave heightsof 10m,12m and 18m are decomposed to series of harmonic wave components byusing ITTC sea spectrum. The heave and pitch motions are obtained by using a linearstrip theory for ship motion under each harmonic wave excitation. The variation ofmetacentic height in each irregular wave is determined by iterating the variations ofmetacentric height for every harmonic wave components. The responses of rollmotion are obtained for the ship in irregular longitudinal waves with respect to theinitial roll angle of 3 degrees and the bias heel angle of 5 degrees which is assumed tobe equivalent to the effect of the wind pressure. The results show that the containership's roll angles come to over 30 degrees under irregular following waves, more over,the capsize of ship is found under the stable crosswind and random wave ofsignificant wave height 18m. The results of the calculation reveal the important effectof the random following wave on the ship rolling and capsizing.