基于随机Melnikov方法的甲板上浪船舶混沌运动研究

应用随机Melnikov方法和庞加莱截面研究甲板上浪时船舶的混沌运动。考虑甲板上浪对船舶静稳性的影响,建立随机横浪中船舶横摇运动方程。由随机Melnikov过程结合均方准则确定船舶产生混沌运动的参数域,计算不同参数域中船舶横摇响应的庞加莱截面和时间历程。结果表明,增加船舶阻尼将抑制混沌运动的发生。甲板上浪时船舶横摇响应的庞加莱截面上有两个吸引域,船舶运动过程有两个横摇中心。在非混沌参数域中,船舶只围绕其中的一个横摇中心运动;在混沌参数域中,发生由一个横摇中心到另一个横摇中心的随机跳跃。

Study on chaotic motion of ship with water on deck using random Melnikov method

Chaotic motion of ship with water on deck is studied using random Melnikov method and Poincare’ map. The roll motion equation of ship in random beam wave is established with considering the effect of trapped water on deck on static stability of ship.The parameter region for chaotic motion of ship is determined by random Melnikov process and mean-square criterion. The Poincare’ map and time history of roll response are calculated in different parameter regions. The results show that the chaotic motion can be restrained when increasing the ship damping. The Poincare’ map of ship roll response has two attraction domains and the roll process has two roll centers when considering the effect of water on deck. In the no-chaotic parameter region, ship rolls around one roll center. In the chaotic parameter region, the random jumping occurs from one roll center to another.