We present a hybrid, semi-analytical approach to perform an eigenvalue-based flutter analysis of an Unmanned Aerial Vehicle (UAV) wing. The wing has a modern design that integrates metal and composite structures. The stiffness and natural frequency of the wing are calculated using a Finite Element (FE) model. The modal parameters are extracted by applying a recursive technique to the Lanczos method in the FE model. Subsequently, the modal parameters are used to evaluate the flutter boundaries in an analytical model based on the p-method. Two-degree-of-freedom bending and torsional flutter equations derived using Lagrange’s principle are transformed into an eigenvalue problem. The eigenvalue framework is used to evaluate the stability characteristics of the wing under various flight conditions. An extension of this eigenvalue framework is applied to determine the stability boundaries and corresponding critical flutter parameters at a range of altitudes. The stability characteristics and critical flutter speeds are also evaluated through computational analysis of a reduced-order model of the wing in NX Nastran using the k- and pk-methods. The results of the analytical and computational methods are found to show good agreement with each other. A parametric study is also carried out to analyse the effects of the structural member thickness on the wing flutter speeds. The results suggest that changing the spar thickness contributes most significantly to the flutter speeds, whereas increasing the rib thickness decreases the flutter speed at high thickness values.

中文翻译：

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一种高展弦比机翼颤振分析的半解析方法

我们提出了一种混合半解析方法来对无人机 (UAV) 机翼进行基于特征值的颤振分析。机翼采用现代设计，融合了金属和复合结构。使用有限元 (FE) 模型计算机翼的刚度和固有频率。通过将递归技术应用于有限元模型中的 Lanczos 方法来提取模态参数。随后，模态参数用于评估基于 p 方法的分析模型中的颤振边界。使用拉格朗日原理导出的二自由度弯曲和扭转颤振方程转化为特征值问题。特征值框架用于评估机翼在各种飞行条件下的稳定性特性。应用该特征值框架的扩展来确定一定高度范围内的稳定性边界和相应的临界颤振参数。还通过使用 k 和 pk 方法对 NX Nastran 中机翼的降阶模型进行计算分析来评估稳定性特性和临界颤振速度。发现分析和计算方法的结果显示出良好的一致性。还进行了参数研究以分析结构构件厚度对机翼颤振速度的影响。结果表明，改变翼梁厚度对颤振速度的贡献最大，而增加肋厚度会降低高厚度值下的颤振速度。