基于CFD降阶的非线性气动弹性稳定性分析

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摘要为了快速寻找基于CFD/CSD的非线性气弹系统的颤振边界，本文根据Lyapunov稳定性理论对非线性流固耦合系统进行稳定性分析。首先通过微扰理论对非线性流固耦合系统处理建立近似线性化状态空间方程，再通过POD (proper orthogonal decomposition)方法将高维状态空间方程降阶为便于分析的降阶系统，根据系统所有特征值即可判定原始非线性系统稳定性。Lyapunov稳定性理论主要针对非线性系统，在实现过程中采用了POD降阶的方法，与大多数对降阶系统稳定性判定不同，其数学理论上是反映原始非线性流固耦合系统稳定性。本文POD降阶方法从系统内部流场出发，可以较好反映系统内部特性。二维三维算例仿真结果验证了本文方法预测颤振边界的正确性，分析发现，在亚音速阶段，稳定性主要由于结构模态主导；而在跨音速和超音速流动阶段，气弹稳定性主要由受流体特性影响。

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	周强
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关键词 ：流固耦合, 李雅普洛夫, 正则正交分解, 状态空间, 颤振

Abstract：In order to quickly find the flutter boundary of a nonlinear aeroelstic system based on CFD/CSD. This paper use Lyapunov stability theory to analyses the stability of nonlinear fluid-structure coupling system. Firstly, through a small perturbation theory, a linearized state space model is obtained based on nonlinear fluid-structure coupling system; then a reduced order model is got by reduce the high dimensional linearized model through a POD (proper orthogonal decomposition) method. According to all the eigenvalues of the ROM system, the stability of the original nonlinear system can be determined. Lyapunov stability theory is mainly aimed at the nonlinear system, and the POD method is adopted to realize the process. Different from other stability methods, the mathematical theory is reflect the stability of the original nonlinear fluid-structure coupling system. As the POD/ROM used in this paper is based on the CFD fluid field, so it can better reflect the internal characteristics of the original nonlinear coupling system. Numerical cases including two dimensional aerofoil and three dimensional wing’s models are tested to validate the accuracy of the stability method. The results show that in subsonic domain, the stability is determined by structural model; But in transonic and supersonic domain, the aeroelastic stability is mainly effected by fluid characteristic.

Key words： Fluid-structure interaction Lyapunov POD state-space flutter

收稿日期: 2015-07-14 出版日期: 2016-08-15

引用本文:

周强，陈刚，李跃明. 基于CFD降阶的非线性气动弹性稳定性分析[J]. 振动与冲击, 2016, 35(16): 17-23.
Zhou Qiang，Chen Gang，Li Yueming. Nonlinear aeroelastic stability analysis based on CFD reduced order models. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(16): 17-23.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2016/V35/I16/17

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