基于Wagner函数的细长机翼非线性空气弹性反应分析

Nonlinear Aeroelastic Response of Slender Wings Based on Wagner Function

介绍了人力飞机机翼的非线性空气弹性分析方法。这种飞机具有长而且高度弹性的机翼。弹性机翼和较长的机翼跨度会在正常飞行中导致机翼的大变形。因此,在机翼的竖向和扭转运动中采用二阶非线性弹性Euler-Bernoulli梁函数进行结构建模。采用基于Wagner函数的不稳定线性空气动力学理论确定机翼的空气动力荷载。将这两种公式结合起来就产生了非线性积分-微分空气弹性函数。采用Galerkin方法和模式求和方法,通过在空间弹性反应分析中引入一个迭代数值方法来求解控制方程。将分析结果与线性分析结果对比,发现在低于颤振速率的速度下,两者能很好地吻合,但是非线性模型显示出机翼的极限周期振幅超出了边界值。

This paper presents a method for nonlinear aero-elastic analysis of Human Powered Aircraft （HPA） wings. In this type of aircraft there is a long, highly flexible wing.Wing flexibility, coupled with long wing span can lead to large deflections during normal flight operation; therefore, a wing in vertical and torsional motion using the second-or- der form of nonlinear general flexible Euler-Bernoulli beam equations is used for structural modeling. Unsteady linear aerodynamic theory based on Wagner function is used for determination of aerodynamic loading on the wing. Combining these two types of formulations yields the nonlinear in- tegro-differentials aeroelastic equations. Using the Galerkin＂ s method and modes summation technique, the governing equations will be solved by introducing an iterative numerical method to predict the aeroelastic response of the problem. The obtained results for a test case are compared with those of linear study which shows good agreement for speeds less than the flutter speed, but the nonlinear model shows limit cycle oscillations for the wing beyond the flutter boundary.