摘要
考虑时变的稳性高GM的影响,导出了传统Spar平台参数激励纵摇运动微分方程,简化得到具有三次非线性项的有阻尼Mathieu方程。应用多尺度法求得了当垂荡频率与纵摇固有频率比接近2∶1时纵摇微分方程的二阶定常响应。根据Floquet理论分析了方程零解与定常周期解的稳定性并进行了数值验证。研究结果表明:稳性高度GM值对于平台纵摇运动的稳定性具有重要影响,调整稳性高度或增加系统阻尼可以减小定常解的不稳定区域,从而抑制平台参数激励纵摇运动的发生。
The parametrically excited differential equation for the pitch motion of a classic Spar platform is established considering the effect of time-varying metacentric height GM value.Then it is simplified to a cubic nonlinear Mathieu equation.The second order steady-state response of the differential equation is solved by the method of multiple scales when the heave frequency is approximately twice as larege as the pitch natural frequency.The stabilities of trivial solution and steady-state periodic solution are analyzed according to the Floquet theory and verified by the numerical method.The result shows that the GM value plays a very important role in the stability of pitch movement.Adjusting GM value or increasing system damping can reduce the unstable region of steady-state solution so as to suppress parametrically excited pitch motion.
出处
《工程力学》
EI
CSCD
北大核心
2010年第3期222-227,共6页
Engineering Mechanics
基金
国家863项目(2007AA09Z30)
国家自然科学基金项目(50879057)
国家自然科学基金重点项目(50639030)
关键词
SPAR平台
非线性Mathieu方程
多尺度法
二阶定常响应
参激纵摇运动
spar platform
nonlinear Mathieu equation
multiple scales
second order steady-state response
parametrically excited pitch motion
