提出了一种针对机翼俯仰和浮沉耦合颤振的跨声速非定常气动力建模方法，将经典的不可压Theodorsen理论扩展到跨声速非定常流。考虑跨声速流压缩效应和非定常下激波运动引起的升力线斜率和焦点变化，构造Theodorsen理论的跨声速修正函数，建立非定常气动力模型，以捕捉跨声速流中非定常气动力幅值和相位的变化。使用Isogai机翼算例模型, 对跨声速修正函数构建、修正函数和非定常气动力的特性、弹性轴的影响、颤振非线性特征等开展了研究。研究结果表明:修正函数能够捕捉跨声速流中翼面激波的振荡特性，非定常气动力的幅值减小和相位滞后；特定弹性轴下获取的修正函数参数值可以泛化到任意弹性轴状态；本文的非定常建模方法能够准确表征跨声速气动力的非线性特性，实现高效准确的跨声速颤振特性预测。
A transonic unsteady aerodynamic modeling method for the coupled pitching and plunging flutter of aircraft wing is pro-posed. This method extends the classical incompressible Theodorsen theory to transonic unsteady flows. By considering the changes of lift-curve slope by compression effect in transonic flows, as well as the shifts of aerodynamic center due to un-steady shock wave movement, a transonic correction function for Theodorsen's theory is constructed, and an unsteady aero-dynamic model is established to capture the changes in the amplitude and phase of unsteady aerodynamic forces in transonic flow. Using the Isogai wing as a case study, research was conducted on the construction of the transonic correction function, the characteristics of the correction function and unsteady aerodynamic forces, the influence of the elastic axis, and the non-linear features of flutter. The results indicate that the correction function effectively captures the oscillatory behavior of shock waves on the wing surface in transonic flow, and the decrease in amplitude and phase lag of unsteady aerodynamic forces. The parameter values of correction function obtained from a specific elastic axis can be generalized to any elastic axis condition. The unsteady modeling method in this paper can accurately represent the nonlinear characteristics of transonic aerodynamic forces and achieve efficient and accurate prediction of transonic flutter characteristics.
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