基于椭圆函数谐波平衡法的二元机翼非线性颤振

针对低阶谐波平衡法精度不高的不足,引入椭圆函数谐波平衡法解决非线性气动弹性问题。基于一阶活塞理论,建立了高速二元机翼的立方非线性颤振方程,采用椭圆函数谐波平衡法、谐波平衡法和Runge-Kutta数值计算方法进行了求解。结果表明：椭圆函数谐波平衡法的计算结果与Runge-Kutta数值计算方法的结果吻合,且与谐波平衡法相比其相对误差更小,可以有效的预测极限环振荡的幅值及其临界点。同时研究了弹性轴位置及重心位置对极限环颤振临界点的影响,随着弹性轴位置不断靠近翼弦中点,极限环振荡临界速度不断增大；而随着重心位置与弹性轴距离的增大,极限环振荡临界速度存在一个极小值点。

FLUTTER ANALYSIS OF 2-D AIRFOIL WITH NONLINEARITIES USING ELLIPTIC HARMONIC BALANCE METHOD

The elliptic harmonic balance method is introduced to solve the nonlinear aeroelastic problem, and the flutter of 2-D airfoil with cubic nonlinear is studied. Firstly, the equilibrium equation of the nonlinear airfoil is established based on the first piston theory, and then solved with elliptic harmonic balance method. The validity of the analytical method is confirmed by comparing the Runge-Kutta (RK) solutions for various values of the vibrational amplitude. And the error is smaller than that of the harmonic balance method. A parametric study is carried out to study the influences of the position of elastic axis and the position of the center of gravity on the flutter velocity. The result shows that flutter velocity strongly depends on the position of elastic axis and the position of the center of gravity. The flutter velocity increases with the elastic axis closing to the airfoil midpoint. And with the center of gravity closing to the elastic axis, there is a minimum value of the flutter velocity.