具有平方阻尼、中心激振非自治系统稳定性研究

Stability Study on a Nonautonomous System with Quadratic Damping and Parametric Excitation

本文研究的数字模型是针对深水海洋张力腿平台的张力腿在涡激下产生的非线性振动问题建立的。该非自治系统具有流体平方阻尼力和中心激振。同时，由非均匀流引起的横向涡激力幅值较小。文中采用Ｋｒｙｌｏｖ－Ｂｏｇｏｌｉｂｏｖ－Ｍｉｔｒｏｐｏｌｓｋｙ近似方法分析，用Ｌｉａｐｕｎｏｖ条件和Ｒｏｕｔｈ－Ｈｕｒｗｉｔｚ法则给出不稳定解存在的范围，并应用数值积分法讨论了稳定解的特性。

he mathematical model used in this paper is aimed at the nonlinear oscillation induced by vortexshedding on the tension Leg Platform. This nonautonomous system has a quadratic fluid damping andparametric excitation, and the vortex excitation force is of very small amplitude.The ssylnptotic method of Krylov-thgoliubov-Mitropolsky(BM) is used as well as Liapunov principle and Routh-Hurwitz criterion for investigation possibility of the tether unstable motion appearen. The4th-order Runge-Kutla numerical method is employed to prove the analytical results and to futher investigate the charactel-istics of some stable solution.