中文摘要：

基于概率理论和非线性动力学方法研究随机横浪中甲板上浪船舶的随机跳跃。应用随机Melnikov均方准则初步划分了船舶发生随机跳跃的参数区域后，由路径积分法求解横摇运动微分方程，得到船舶横摇响应的联合概率密度函数。通过概率密度函数的形状和庞加莱截面判定船舶横摇运动的随机跳跃，并由时间历程进一步验证了结论的可靠性。研究表明，有甲板上浪时船舶横摇响应的联合概率密度函数有两个峰，船舶运动过程有两个可能的横摇状态。在非混沌参数区域中，这两个峰不相通，船舶运动只实现其中的一个状态而不发生跳跃。在混沌参数域中，当波浪激励达到一定强度时，这两个峰相通，船舶运动在这两个状态间随机跳跃，这将引发船舶的不稳定运动甚至导致倾覆。

英文摘要：

The random jumping of ships with water on deck in random beam waves is studied based on the probability theory and nonlinear dynamic method. The parameter region for random jumping of ships is demarcated primarily by the random Melnikov mean-square criterion. The probability density function of the roll response is calculated by solving the differential equation of ships rolling using the path integral method. The random jumping is judged by the shape of the probability density function and the Poincare maps, and the conclusions are verified by the time histories of the system. It is found that the joint probability density function of ship roll response with water on deck has two peaks, and ship motion process has two possible roll states. In the no-chaotic parameter region, the two peaks are unconnected, only one roll state can be achieved and no jumping occurs. In the chaotic parameter region, when the wave excitation is strong enough, the two peaks are connected and ship motion jumps randomly from one roll state to another. This will lead to instability and even capsizing.