GZ曲线分段线性化对船舶横摇运动响应的影响研究

Research on the Influence of Piecewise Linearization of the GZ Curve on the Response of Ship Rolling Motion

大幅横摇运动是导致船舶倾覆的主要原因之一.对于瘫船模型,学术界提出了分段线性化方法计算船舶倾覆概率.该方法采用随机线性化方法近似横摇非线性阻尼,并将复原力臂曲线(GZ曲线)进行分段线性化处理,从而得到横摇运动方程的解析解.文中采用路径积分法对控制横摇运动微分方程概率属性的Fokker-Planck方程进行求解,获得了随机载荷作用下准确的船舶横摇运动响应.并根据路径积分法计算得到的平均穿越率和谱分析方法,研究了GZ曲线分段线性化对横摇运动响应的影响.结果表明:GZ曲线的分段线性化近似将对船舶横摇运动响应极值造成显著影响.

Large amplitude roll motion is one of the main reasons leading to ship capsize.For the dead ship model,the piecewise linearization method has been proposed by the academia in order to calculate the capsizing probability.In this method,the statistical linearization procedure was applied to approximate the nonlinear roll damping items and the restoring curve(GZ curve)was simplified by means of piecewise linearization in order to obtain the analytical solution of the differential equation for the roll motion.In this work,the path integration(PI)approach was introduced in order to solve the Fokker-Planck equation,which governs the probabilistic properties of the differential equation for the roll motion.Therefore,the response of the roll motion under random excitation can be accurately obtained.According to the mean up-crossing rate calculated by path integral method and spectral analysis method,the influence of piecewise linearization of the GZ curve on the roll response was investigated.The results show that piecewise linearization of the GZ curve has a significant influence on the extreme roll response.