In this paper, by defining a new paradigm for nonlinear aerodynamic equations of flow separation and static stall, a new form of nonlinear aeroelastic equations for a highly flexible composite wing with torsional and bending movement is presented. Structural modeling is carried out using nonlinear general flexible Euler–Bernoulli beam equations in the third-order. Combining the unsteady Wagner model and the nonlinear lift coefficient-angle of attack lead to the aerodynamic equations for simulating stall using a cubic approximation. The aeroelastic equations are obtained utilizing Hamilton’s principle and Lagrange equations. A time-history integration method is used to solve the integro-differential nonlinear aeroelastic equations. The obtained results are compared with previous studies for validation, and there is good agreement between the results. The results show that the use of the cubic curve instead of the piecewise linear curves which is commonly used in other references, although, causes an apparent complication of the equations but reduces the errors. It is also observed that the limit cycle oscillations speed changes by changing the angle of fibers, and the maximum of this instability speed occurs at an angle of about twenty degree.

在本文中，通过为流分离和静态失速的非线性空气动力学方程式定义新范式，提出了一种新的形式的具有挠曲和弯曲运动的高柔性复合材料机翼非线性空气弹性方程式。使用三阶非线性通用弹性Euler-Bernoulli梁方程进行结构建模。将非平稳瓦格纳模型和非线性升力攻角相结合，得出了用三次近似法模拟失速的空气动力学方程。空气弹性方程是利用汉密尔顿原理和拉格朗日方程获得的。使用时间历史积分方法求解积分微分非线性气动弹性方程。将获得的结果与以前的研究进行比较以进行验证，结果之间有很好的一致性。结果表明，尽管使用三次曲线代替了其他参考文献中常用的分段线性曲线，但显然会引起方程式的复杂化，但会减少误差。还观察到极限循环振荡速度通过改变纤维的角度而变化，并且该不稳定性速度的最大值在约二十度的角度处发生。