中文摘要：

研究了随机纵浪中船舶的参数激励横摇运动。将船舶初稳性高作为时变的随机参数激励，应用随机平均法和FPK方程，分析了船舶的参数激励横摇运动微分方程。考虑航速、船舶瞬时湿表面积及随机波浪，建立了船舶横摇幅值概率密度、概率分布函数及其均值的计算方法。以某渔政船为例，计算了不同航速时船舶随机横摇幅值的概率密度、概率分布函数及其均值。结果表明，参数激励谱峰频率为横摇固有频率的2倍时，发生主参数共振，船舶横摇严重，船舶倾覆发生的概率增加。

英文摘要：

Parametrically excited ship rolling in longitudinal waves is studied. The parametrically excited rolling equation of ships considering the metaeentric height variation with time is analyzed using stochastic averaging method and FPK equation. The probability density function, probability distribution function and the mean value of stochastic roll amplitude are educed taking account of ship speed, instantaneous wet area and stochastic waves. Taking a fishery administration ship for example, the probability density function, probability distribution function and the mean value of the stochastic roll amplitude under different navigation speeds are obtained. The results show that when the frequency corresponding to the peak value of the parametric excitation spectrum is near the twice of roll natural frequency, the principal parametric resonance occurs, and the large amplitude rolling arises which results in the increase of ship capsize probability.