基于曲梁模型的大展弦比大柔性机翼颤振分析

摘要

A method for flutter of the very flexible wing with a high⁃aspect⁃ratio is developed. Firstly, the very flexi⁃ble wing subjected to aeroelastic load will undergo a large deformation. So the deformed wing can be regarded as a curve beam and divided into a couple of curve beam elements. The mean curvature of every beam element is ob⁃tained by mean of polynomial interpolation method. For each element, the flutter differential equations is established by combining the differential equations of the constant curvature beam vibration and the Therdorson'unsteady aero⁃dynamics model. Then, using the distributed transfer function method and the finite element method, the equilibri⁃um equations of the whole wing are obtained. Finally, the wing flutter was carried out by solving a eigenvalue prob⁃lem. The results are good agreement to the literature solutions and indicate that the present method is accurate and efficient.%提出一种大展弦比大柔性机翼颤振分析的方法。该方法首先引入准模态假设，将气动载荷作用下发生大静变形的大展弦比大柔性机翼视为一根变曲率曲梁，并将其离散为一系列常曲率曲梁单元，利用机翼静变形结果，通过多项式插值获得各曲梁单元的平均曲率。其次，在曲梁单元内，利用曲梁振动微分方程和Therdorson非定常气动力模型建立曲梁单元的颤振微分方程。然后，运用传递函数法，将曲梁单元的颤振微分方程转换为状态空间形式，并依照有限元组集的思想形成机翼整体平衡方程。最后，通过求解特征值问题获得机翼的颤振速度和颤振频率。通过与已有文献结果的对比，验证了新方法的正确性和有效性。