An empirical modeling of nonlinear aerodynamic force during aeroelastic instabilities, that is, vortex-induced vibration (VIV), galloping and flutter, is necessary in the estimation of vibration responses. Previous works on single-degree-of-freedom (SDOF) models suggest that nonlinear forms (Van der Pol or Rayleigh types) differ from section to section, which causes difficulty in practical application. Analytical evidences in this study have clarified that Van der Pol-type and Rayleigh-type models are equivalent in the amplitude-dependent aerodynamic damping; their difference lies in the higher-order harmonic responses. An identification algorithm of aerodynamic parameters is proposed to improve the robustness of aerodynamic parameters and guarantee the equivalence of both model types. Wind-tunnel tests of typical aeroelastic instabilities indicate that higher-order harmonic responses are small for VIV, galloping, and early-stage flutter instability when compared with the fundamental components due to weak nonlinearity. Van der Pol-type and Rayleigh-type models are both applicable until the flutter amplitude grows excessively large. It is clear that both model types are suitable for any section shape when use the proposed method of aerodynamic identification, and thus can be treated as a universal model for estimating the vibration amplitudes of nonlinear aeroelastic instabilities.

在估计振动响应时，需要对气动弹性不稳定期间的非线性气动力进行经验建模，即涡激振动 (VIV)、飞驰和颤振。以前关于单自由度 (SDOF) 模型的工作表明，非线性形式（Van der Pol 或 Rayleigh 类型）因截面而异，这给实际应用带来了困难。本研究的分析证据表明，Van der Pol 型和瑞利型模型在依赖于振幅的气动阻尼方面是等效的；它们的区别在于高次谐波响应。提出了一种气动参数辨识算法，以提高气动参数的鲁棒性，保证两种模型类型的等效性。典型气动弹性不稳定性的风洞试验表明，由于弱非线性，与基本分量相比，VIV、飞驰和早期颤振不稳定性的高次谐波响应较小。Van der Pol 型和瑞利型模型都适用，直到颤振幅度变得过大。很明显，当使用所提出的空气动力学识别方法时，这两种模型类型都适用于任何截面形状，因此可以被视为估计非线性气动弹性不稳定性的振幅的通用模型。Van der Pol 型和瑞利型模型都适用，直到颤振幅度变得过大。很明显，当使用所提出的空气动力学识别方法时，这两种模型类型都适用于任何截面形状，因此可以被视为估计非线性气动弹性不稳定性的振幅的通用模型。Van der Pol 型和瑞利型模型都适用，直到颤振幅度变得过大。很明显，当使用所提出的空气动力学识别方法时，这两种模型类型都适用于任何截面形状，因此可以被视为估计非线性气动弹性不稳定性的振幅的通用模型。