深海顶张力立管Mathieu不稳定性研究(英文)  

Mathieu Instability Analysis of Deepwater Top-tensioned Risers

作　　者：张杰[1] 唐友刚[2] 

机构地区：[1]上海海事大学海洋科学与工程学院,上海201306 [2]天津大学建筑工程学院,天津300072

出　　处：《船舶力学》2014年第9期1142-1150,共9页Journal of Ship Mechanics

基　　金：Supported by the National Nature Science Foundation of China(51079097);Top Discipline Projects of Shanghai Municipal Education Commission;The Innovation Projects of 2013 Shanghai Postgraduate Education(the second,20131129)

摘　　要：Mathieu方程是描述单自由度参数振动系统的经典方程,但立管属于多自由度系统,参数激励作用下立管横向振动方程是四阶周期性变系数偏微分方程。文章首先通过Garlkin方法将立管运动偏微分方程转化为Mathieu方程,依据Mathieu不稳定图对立管每一阶模态进行独立分析后叠加得到立管的不稳定图,并与基于Floquet理论的数值计算结果进行对比。研究结果表明,立管各模态不稳定区存在大量重叠区域,由于高阶不稳定区范围狭窄且在阻尼作用下迅速减小,实际应用中,可只考虑立管一阶不稳定区。立管系统参数设计应尽量避免落在参数不稳定区。Mathieu equation is the classic differential equation with periodic coefficients, which governs the response of many physical systems having one degree of freedom. However, the riser is a multi-degree of freedom system. The equation of transverse motion of a riser under parametric excitations is a fourth-order partial differential equation containing a time-dependent coefficient. Firstly, this equation is reduced to Mathieu equation by using the Galerkin method. According to Mathieu instability chart, every mode is analysed in the same manner as the system with one-degree of freedom, and the parametric instability chart of the riser is obtained by mode superposition. In addition, the results are compared with those obtained by numerical simulation based on the Floquet theory. The results show that natural frequencies of the riser are very dense due to the high slenderness ratio, which leads to overlapping of different instability zones. The first instability zones are more important than higher instability zones which are very narrow in the instability charts. Special attention on the system parameters is needed for designers to avoid vibration instability.

关 键 词：深海立管 MATHIEU方程 参激稳定性 动力响应 

分 类 号：TE58[石油与天然气工程—油气田开发工程] O323[理学—一般力学与力学基础]