Abstract Nonlinear effects such as friction and freeplay on the control surfaces can affect aeroelastic dynamics during flight. In particular, these nonlinearities can induce limit cycle oscillations (LCO), changing the system stability, and because of this it is essential to employ computational methods to predict this type of motion during the aircraft development cycle. In this context, the present article presents a matrix notation for describing the Henon’s method used to reduce errors when considering piecewise linear nonlinearities in the numerical integration process. In addition, a new coordinate system is used to write the aeroelastic system of equations. The proposal defines a displacement vector with generalized and physical variables to simplify the computational implementation of the Henon’s technique. Additionally, the article discusses the influence of asymmetric freeplay and friction on the LCO of an airfoil with control surface. The results show that the extended Henon’s technique provides more accurate LCO predictions, that friction can change the frequency and amplitude of these motions, and the asymmetry of freeplay is important to determine the LCO behavior.

中文翻译：

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摩擦和非对称自由游隙对气动弹性系统极限循环振荡的影响：一种扩展的 Hénon 时间积分技术

摘要 控制面上的摩擦和自由间隙等非线性效应会影响飞行过程中的气动弹性动力学。特别是，这些非线性会引起极限循环振荡 (LCO)，从而改变系统稳定性，因此在飞机开发周期中必须采用计算方法来预测此类运动。在这种情况下，本文提出了一种矩阵表示法，用于描述在数值积分过程中考虑分段线性非线性时用于减少误差的 Henon 方法。此外，使用新的坐标系来编写气动弹性方程组。该提议定义了一个具有广义和物理变量的位移向量，以简化 Henon 技术的计算实现。此外，本文讨论了非对称自由间隙和摩擦对带控制面的翼型的 LCO 的影响。结果表明，扩展的 Henon 技术提供了更准确的 LCO 预测，摩擦可以改变这些运动的频率和幅度，并且自由间隙的不对称性对于确定 LCO 行为很重要。