船舶甲板上浪的非线性横摇响应

Nonlinear roll response of ship with water on deck

考虑甲板上浪引起的横倾力矩、非线性阻尼和非线性恢复力矩,建立了规则横浪中船舶横摇运动方程;基于伯努利方程,推导了船舶甲板上浪水质量的计算公式。以66.01米长的拖网渔船为例,计算了不同波浪扰动力矩作用下的横摇响应,并构造了响应的分岔图和庞加莱截面。结果表明:甲板上浪后船舶横摇运动包括混沌运动和周期二、周期三、周期四等多周期运动;随着波浪扰动力矩幅值的增大,横摇响应发生从周期运动到混沌运动或从混沌运动到周期运动的阵发性分岔、正向及反向倍周期分岔。

The nonlinear dynamical behaviors of multi-periodic motion, bifurcation and chaos of ship rolling are studied when water on deck occurs. The roll motion equation of ship in beam wave is established by considering the heeling moment due to the water trapped on deck, the nonlinear damping and the nonlinear restoring moment. The formula for calculating the mass of water trapped on ship deck is derived based on the Bernoulli equation. Taking a trawl ship of 66.01 meters in length as an example, roll responses excited by different wave disturbance moment are calculated, the bifurcation diagrams and Poincare′ maps are constructed. It is found that the roll responses of ship with water on deck include chaotic motion and multi-periodic motion, such as period-two, period-three and period-four motion. When the amplitude of wave disturbance moment is increased, the explosive bifurcation of periodic motion to chaotic motion or chaotic motion to periodic motion and period-doubling or inverse period-doubling bifurcation are found in roll response.