基于传递函数法的带多个外挂机翼颤振分析

基于带外挂机翼结构和气动特点,使用带有半解析半数值特性的传递函数方法进行处理.首先,通过机翼的运动微分方程、二元机翼非定常气动力Therdorson模型、结合外挂挂载处的内力平衡与位移状态条件,得到了三维的带多个外挂大展弦比机翼的颤振微分方程.进而,使用传递函数方法,先将颤振计算方程整理成为状态空间方程形式,结合求解复特征值的方法,完成了带多个外挂大展弦比机翼的动气动弹性稳定性分析.对比已有文献的计算结果以及通过有限元方法进行的仿真结果,证实了文章所提计算方法的准确性和高效性,结合传递函数方法的优势,进一步将文章方法拓展到机翼的固有频率和发散速度求解.文章结尾,分析了外挂数量、外挂质量、转动惯量及位置分布等变量对带多个外挂大展弦比机翼的动气动弹性稳定性的影响.

Analysis of the Flutter of a Wing with Many External Stores by Transfer Function Method

The semi-analytical and semi-numerical transfer function method is applied to the flutter of a high-aspect-ratio aircraft wing with many concentrated external stores. Firstly, the flutter differential equation of a three-dimensional wing is established by combining the bend-twist vibration equations of the wing, the Therdorson unsteady aerodynamics model for the clean wings and the deformation harmony and internal force balance conditions on the position of the external store. Then, the control equations are formulated in a state-space form by defining a state vector by the transfer function method. Combined with the method of solving complex eigenvalues, both the flutter velocity and flutter frequency are obtained. The results are in good agreement with the literature solutions and the finite element method solutions, which proves that the present method is correct and efficient. Additionally, the torsion divergence and the natural frequency of the aircraft wing can be easily obtained by the transfer function method. Finally, the effects of quantity, the mass, the moment inertia and the position of the external stores are investigated.