中文摘要：

采用概率密度函数和数值模拟的方法研究随机横浪中船舶的混沌运动特性和发生混沌运动的临界参数条件。综合考虑非线性阻尼、非线性恢复力矩以及白噪声横浪激励,建立了船舶的横摇非线性随机微分方程。用随机Melnikov均方准则确定混沌运动的系统参数域后,应用路径积分法求解随机微分方程得到了响应的概率密度函数。研究发现：当噪声强度大于混沌临界值时,船舶出现随机混沌运动;对于高的白噪声激励强度,系统响应有两种较大可能的状态并在这两个状态间随机跳跃,这时船舶的运动不稳定并可能发生倾覆。

英文摘要：

The stochastic chaotic motion and the threshold parameter value for ships onset chaotic motion in random beam waves are studied by the probability density function and the numerical method. The random differential equation of ships＇ rolling motion is established with considering the nonlinear damping, nonlinear restoring moment and the white noise wave excitation. The random Melnikov mean-square criterion is used to determine the threshold parameters for the ships＇ stochastic chaotic motion. The probability density function of the rolling response is calculated through solving the stochastic differential equations by the path integral method. It is found that the ships undergo stochastic chaotic motion when the real intensity of the white noise exceeds the threshold value. For high intensity of white noise excitation, the stable probability density function has two peaks and the response of the system may jump from one high probability state to another. That will lead ships to instability and even to capsizing.