中文摘要：

该文从船舶非线性横摇运动方程出发,采用多尺度法,获得其在正横规则波中的超谐共振稳态解,并将其作为液舱运动的外部激励。在此基础上,基于Open FOAM开源代码,采用基于VOF的两相流模型模拟液舱内气液运动,研究了船舶在超谐共振横摇条件下的液舱晃荡动特性问题。结果表明,在超谐共振横摇条件下,自由液面易出现翻卷、破碎等强非线性现象,舱壁压力时历表现出多峰型特征,其峰值要远大与简谐激励的情况,而且舱内液体晃荡在两个谐波成分的差频附近发生共振响应。

英文摘要：

Based on nonlinear equation of the ship rolling motion, a super-harmonic resonance steady-state solution of the rolling motion in the regular beam waves by multiscale method is obtained, and then such a solution is regarded as an external excitation of a partial filled tank. Based on VOF method for simulating the gas-liquid two phase flow in the tank, the characteristics of the tank sloshing under super-harmonic rolling motion are analyzed by use of Open FOAM open source code. The results show that under super-harmonic rolling, the characteristics of the free surface are characterized by strong nonlinear phenomena, such as turning up and breaking. Moreover, the dynamic pressure on the tank wall shows the characteristics of multiple peaks and its peak value is much larger than one for harmonic excitation. In particular, the resonance phenomenon happens when the natural frequency of the partial filled tank is equal to difference frequency of two harmonic waves in super-harmonic rolling motion.