随机波浪作用下船舶倾覆的量化研究

Quantitative study on safety degree of ship capsizing in stochastic waves

为量化船舶倾覆问题,基于随机迈尔尼科夫(Melnikov)函数和相空间传输理论,从能量的角度对随机波浪下船舶航行时倾覆发生的安全程度进行研究.考虑阻尼力矩和回复力矩的非线性以及波浪的随机性,建立船舶非线性横摇运动微分方程.采用快速傅里叶变换(FFT)将时域波浪力转换到频域,从而将随机Melnikov函数及相空间转移率扩展到考虑船舶航速和浪向角的影响,并根据其统计特性对船舶倾覆进行量化.通过实船算例研究其在随机海浪中横摇运动相空间转移率的变化情况,并分析船舶航速、遭遇浪向以及波浪特征频率对相空间转移率的影响.研究结果表明,随机Melnikov函数和相空间传输理论能够较好地对具有一定航速的船舶在随机波浪中的倾覆进行量化,从而可为进一步研究船舶稳性衡准提供有益的参考.

To quantify safety problem of ship capsizing,the safety degree of a ship sailing in random waves was studied based on stochastic Melnikov function and phase space transport theory from the energy perspective.Considering the nonlinear damping moment,nonlinear righting moment,as well as the random waves,a nonlinear single degree of freedom differential equation of ship rolling was established.The random wave-induced moment was transformed from time domain to frequency domain by using FFT,and the random Melnikov function and the rate of phase flux were extended to effects of navigation speed and heading angle.The safety degree of a ship against capsizing was quantified according to the statistical properties.Based on studying the parameters of a typical ship,the variation of rolling phase space transport rate in stochastic waves was investigated,and the effects of ship speed,heading angle and wave characteristic frequency were analyzed.Research results show that the Melnikov function and random phase space transport theory are available to quantify the safety degree of a ship against capsizing,and then to provide beneficial reference for the further investigation on ship stability criteria.