为了快速寻找基于 CFD／CSD 的非线性气弹系统的颤振边界，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。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该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。%In order to quickly find the flutter boundary of a nonlinear aeroelstic system based on CFD /CSD,this paper used the Lyapunov stability theory to analyze the stability of a nonlinear fluid-structure coupling system.Firstly,a linearized state space model was obtained based on a nonlinear fluid-structure coupling system through the small perturbation theory;then a reduced order model was achieved by reducing the high dimensional linearized model through a POD(proper orthogonal decomposition)method.According to the eigenvalues of the ROM system,the stability of the original nonlinear system could be determined.Lyapunov stability theory was mainly aimed at the nonlinear system,and the POD method was adopted to realize the process.Different from other stability methods,the mathematical theory reflected the stability of the original nonlinear fluid-structure coupling system.As the POD /ROM used in this paper was based on the CFD fluid field,so it could better reflect the internal characteristics of the original nonlinear coupling system.Numerical cases including two-dimensional aerofoil and three-dimensional wing's models were used to validate the accuracy of the stability method.The results show that in the subsonic domain,the stability is determined by the structural model;but in transonic and supersonic domain,the aeroelastic stability is mainly affected by fluid characteristics.
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