舰船横摇垂荡非线性耦合的动力不稳定区域

研究了横摇和垂荡非线性耦合情况下的动力不稳定区问题，在船舶顶浪情况下，采用约束参数法分别对非线性耦合和线性耦合的方程进行了稳定性分析，得到稳定区域传递曲线方程。用龙格－库塔数值积分方法分别对此两类方程选择多种类型参数值进行摇摆响应分析，观察到横摇回复运动、周期稳态运动、以及混沌和倾覆等现象，验证了理论分析的结果，理论与数值分析表明，横摇和垂荡的非线性耦合对于船舶摇摆是不可忽略的非线性因素，采用约束

Instability of Ship Roll with Nonlinear Heave-Roll Coupling

Study on the instability regions of ship rolling with nonlinear coupling of heave and roll was presented. The Hill's equation, which describes not only the linear but also the quadratic coupling term, was developed from the heave roll coupled governing equations of a vessel in head sea to simulate the parametrically excited system of the roll motion coupled with heave. And the Mathieu's equation, including only the linear coupling term, was also developed. Using the method of strained parameters for the two types of the parametrically excited systems including nonlinear and/or linear coupling term, the stability regions were derived. The results were verified by numerical analysis using Runge Kutta method with the parameters on the margins or in out of the instability regions. The periodic steady state solutions, the convergent solutions, the divergent solutions and the chaotic solutions for the ship roll response were reported. It is shown by the theoretical and numerical investigation that the nonlinear coupling term is a very important factor to ship motion, and the methods of strained parameters is effective in the analysis of stability of ship rolling.