本研究利用解析的方法將尾流運動方程、葉片空氣動力學、ONERA動態失速模式及一個非線性複材葉片的結構運動方程整合成一耦合的非線性系統。利用Galerkin法及Duncan多項式將其展開，並分成非線性平衡態及線性擾動態兩種方程式。而非線性平衡態部份將利用數值法求出與時間無關之係數；再求取該耦合模式的平衡態的解。平衡態的具體結果包含了在此非穩態空氣動力系統及動態失速之下的旋翼葉片在懸停時，其尖端的位移值，此數據一方面可提供擾動態求解特徵值(包含阻尼) ，一方面也藉此觀察動態失速在前飛時對旋翼葉片的影響，並尋求物理現象之解釋。而從葉片位移的角度來分析問題，是一個比較具體且具說服力的方式，對於該物理現象有定性及定量的描述。 An eigen-analysis provides stability information for a rotor system, and it is also an important part of rotor aeroelastic analysis. The resonance phenomenon can be predicted by eigen-analysis as well. In this research, a new three-dimensional wake and nonlinear composite rotor blade flap-lag-torsion coupled model will be developed. The generalized dynamic wake model employed is based on an induced undetermined time dependent coefficients as aerodynamic states. The Galerkin's method and Duncan polynomials are used to expand this nonlinear coupled equation into equilibrium and disturbant parts. The nonlinear phenomenon will be investigated through eigen-analysis, especially for nonlinear resonance. Hopefully, some of the physical meanings behind the nonlinear resonance would be discovered through eigen-value point of view.
