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中文摘要：
研究了涡激力作用导致顶张力立管基于双频激励的参量共振机理。随着海洋油气开发走向深水,参量共振成为深海立管设计面临的挑战之一。立管系统一旦发生参量共振,将因应力过大或疲劳损伤而发生破坏,造成油气泄漏从而带来环境污染和重大经济损失。顶张力立管受涡激力作用产生横向运动,引起轴向张力波动,满足一定条件时,立管将发生参量共振。目前研究多以单频外激励探讨立管的马修不稳定性,而实际激励为多频叠加,因此双频外激励被提出并被应用于对立管参量稳定性的探讨。研究建立了顶张力立管非线性耦合的运动方程,并推导了多频激励马修方程,采用布勃诺夫-伽辽金法求解有阻尼马修方程,对比分析了单频和双频激励对顶张力立管参量稳定性的影响,探讨了双频激励马修方程设计深海顶张力立管参量稳定性的应用。研究表明：涡激致顶张力立管产生轴向应力波动,进而导致立管系统发生参量共振的现象值得设计人员关注;此外,实际工程设计中激励函数的选取,对被研究系统参量稳定性特性以及阻尼特性的预测具有决定性影响。
英文摘要：
Parametric resonance of Top Tensioned Riser（TTR） induced by vortex-induced force based on bi-frequency excitation is studied. Parametric resonance is a challenge for riser designing as the exploration of oil/gas approaches deeper water. Once parametric resonance occurs, the riser shall encounter damage due to excessive stress or significant fatigue, and catastrophe follows. Subjected to vortex-induced force, axial tension fluctuation also takes place because of TTR＇s lateral motion; when a certain condition is satisfied, parametric resonance occurs. Nowadays, researchers tend to predict the excitation using a single frequency function, while the real one is a superposition of many frequencies, namely multi-frequency, thus the hi-frequency excitation is proposed and used for TFR＇s para- metric resonance study. For the present problem, a nonlinear coupled governing equation is obtained, then Mathieu equation of multi- frequency excitation is derived. The equation is solved by Bubnov-Galerkin method. Comparative analysis on the influence of single-or bi-frequency excitation on the system＇s parametric stability is done, then the designing application of Mathieu equation of bi-frequency excitation to deepsea risers is discussed. The results show that the phenomenon of riser system＇s tension fluctuation and the worse parametric resonance, induced by vortex excitation, deserves to be concerned by designers ; Meanwhile, during the process of ＇ITR design, the selection of the excitation function is vital to the prediction of the parametric stability and damping for a system.
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