大展弦比带外挂机翼的颤振分析
Flutter Analysis of a High-aspect-ratio Wing with External Store

基于哈密顿原理推导建立大展弦比带外挂机翼的动力学方程。为了分析大展弦比机翼特性，考虑了大展弦比机翼的平面内弯曲效应，将传统机翼的弯扭动力学方程扩展到大展弦比机翼的弯弯扭方程；利用Dirac函数考虑外挂位置的影响；采用拉格朗日乘子的方法考虑梁模型轴向不可伸缩约束。引入无量纲化参数对动力学方程进行无量纲化处理。基于梁模型的边界条件，利用伽辽金方法及主振型的正交性将偏微分方程离散为常微分方程，并改写成矩阵和状态方程的形式。利用K方法进行颤振计算，分析外挂参数如外挂质量、位置和转动惯量对机翼外挂系统颤振速度的影响，并分析了各种速度条件下的响应历程。
The kinetic equation of the high-aspect-ratio wing with an external store is derived based on Hamilton's principle. This paper considers the in-plane bending of the high-aspect-ratio, and extends the bending-torsion motion of the traditional wing to bending-bending-torsion motion of the high-aspect-ratio wing. Dirac function is used to precisely consider the location and properties of the external store. The constraint of the beam is considered with the Lagrange multiplier method. The dimensionless dynamic equation is conducted by the introduction of dimensionless parameters. The Galerkin method is subsequently applied to convert to partial differential equations into a set of ordinary differential equations. The flutter is calculated with the K method. The linear system simulation results are presented to show the linear flutter velocity and then the effects of the store properties, such as location and mass on the wing store linear flutter velocity are also given