水下爆炸及随机外力下破损舰船的倾覆概率分析

摘要

The calculation of capsizing probability of damaged warship subjected to underwater explosions and random excitations was discussed.The nonlinear differential equation of ship's roll motion under the conditions of underwater explosions and random excitations was established,in which the effect of underwater explosions and average wind disturbing moment were considered as constant heeling moments. Using the method of extended dimension number, the roll equation was transformed to five dimension Ito stochastic differential equation.Probability density function of rolling angle changed with time was presented based on Ganss-Legendre path integration method,when the random disturbance was reduced to white noise. And the expression of capsizing probability of warship was obtained on the basis of the existent capsizing criterion.An example for calculating the capsizing probability of damaged warship subjected to weapon attack with different blasting charge at different time was given and the effect of blasting charge on capsizing probability was analyzed.The study shows that this method could easily predict rolling capsizing probability of damaged warship subjected to underwater explosions and random excitations quantitatively. It is helpful to further research of capsizing and stability.%探讨了水下爆炸载荷和随机风浪联合作用下破损舰船的运动及其倾覆概率的计算.将爆炸载荷作用及平均风扰动力矩处理为定常横倾力矩,建立了爆炸载荷和随机风浪中舰船运动的非线性微分方程.结合扩维技巧,将横摇方程转化为五维Ito随机微分方程,应用Gauss-Legendre路径积分法给出随机扰动为白噪声时横摇角度的概率密度函数随时间的演变,按照现有的倾覆准则给出预报一定装药量下舰船倾覆概率的表达式.通过算例,计算了破损舰船不同装药量下不同时刻的倾覆概率,分析不同装药量对倾覆概率的影响.研究表明,此方法简便可行,并能在数量上预报破损舰船在水下爆炸及随机风浪下的倾覆概率,为进一步研究舰船倾覆及稳性横准提供有益的参考.