带外挂机翼的极限环颤振分析

LIMIT CYCLE FLUTTER ANALYSIS OF A WING WITH AN EXTERNAL STORE

首先基于哈密顿原理推导带外挂机翼的弯扭动力学方程。利用Dirac函数考虑外挂位置的影响;采用拉格朗日乘子方法考虑梁模型轴向不可伸缩的约束;带外挂机翼的动力学方程考虑了结构非线性、气动非线性和外挂非线性,并将非线性的阶数扩展为3阶。其次引入无量纲化参数对动力学方程进行无量纲化处理。最后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方法进行线性颤振的计算;选取弯曲运动速度为零的点作为Poincare截面点,基于分叉图来研究带外挂机翼弯曲、扭转的极限环颤振特性。

The kinetic equations of the wing with an external store based on Hamilton＇ s principle are derived. Dirac function is used to precisely consider the location and properties of the external store. And the constraint of the beam is considered with the Lagrange multiplier method. The structure nonlinear, aerodynamic nonlinear and store nonlinear will be all considered in the kinetic equations of the wing store system, and the nonlinear equation will include all nonlinearities up to third order. The dimensionless of the dynamic equation is conducted by the introduction of dimensionless parameters. Based on the boundary conditions of the beam, the Galerkin method is subsequently applied to convert to partial differential equations into a set of ordinary differential equations, and then rewrite the equation in the form of matrix and state equation. The linear flutter is calculated by use the k method; By selecting the bending speed zero point as the Poincare section, the bifurcation diagram can be given the limit cycle flutter characteristics of the bending and torsion motion.