This study performs an experimental and numerical investigation on the nonlinear aeroelastic response of cantilever high-aspect-ratio beam-like wings with a ballast at their free tips, emulating the effects of a store. As an extent, the effects of different chord-wise ballast positions are experimentally examined for two highly flexible rectangular wings. Furthermore, the numerical model proposed brings forward a nonlinear finite element beam model accounting for aerodynamic nonlinearities, via stall and follower forces models, along with geometrical nonlinearities due to large displacements and rotations. A great variety of analyses were performed: First, the flutter boundaries of the wings were analyzed; second, the limit cycle oscillation amplitudes and frequencies in the oscillating wings were evaluated; third, the coupling behavior and the nonlinear responses obtained were discussed under several attributes. The geometrical nonlinearities were taken into account by a total Lagrangian formulation based on a straightforward and consistent interpolation field in order to describe the exact kinematics of a Timoshenko’s beam. Nonlinear aerodynamic loads were computed via an unsteady strip theory in the time-domain with the Jones approximation for the Wagner’s function along with a follower aerodynamic loads assumption. Additionally, a non-usual stall model based on an experimental quasi-static stall curve for flat plates was used to interpolate the lift-curve slope. The experimental and numerical results indicated a minimum flutter speed for ballast positions about of $-5$ mm toward the leading edge. Next, different nonlinear post-flutter LCO behaviors were obtained for the different ballast positions tested. To conclude, the good correlation between model and experiments indicated that the nonlinear modeling approach proposed herein was capable to predict the aeroelastic behavior of the tested high aspect-ratio wings.

这项研究对悬臂式高纵横比梁形机翼的自由末端带有压载物的非线性气动弹性响应进行了实验和数值研究，模拟了存储的影响。在一定程度上，通过实验检查了两个高柔韧性矩形机翼不同弦向压载位置的影响。此外，提出的数值模型通过失速和从动力模型提出了考虑到空气动力学非线性的非线性有限元梁模型，以及由于大位移和旋转而引起的几何非线性。进行了各种各样的分析：首先，对机翼的颤振边界进行了分析；其次，评估了摆动翼的极限循环振荡幅度和频率。第三，在几个属性下讨论了耦合行为和获得的非线性响应。基于简单一致的插值场的总拉格朗日公式考虑了几何非线性，以便描述蒂莫申科光束的精确运动学。非线性气动载荷是通过时域中的非定常带理论，利用Wagner函数的Jones近似以及跟随者气动载荷假设来计算的。此外，基于实验准静态失速曲线的平板非常规失速模型用于内插升力曲线斜率。实验和数值结果表明，镇流器位置的最小颤动速度约为 基于简单一致的插值场的总拉格朗日公式考虑了几何非线性，以便描述蒂莫申科光束的精确运动学。非线性气动载荷是通过时域中的非定常带理论，利用Wagner函数的Jones近似以及跟随者气动载荷假设来计算的。此外，基于实验准静态失速曲线的平板非常规失速模型用于内插升力曲线斜率。实验和数值结果表明，镇流器位置的最小颤动速度约为 基于简单一致的插值场的总拉格朗日公式考虑了几何非线性，以便描述蒂莫申科光束的精确运动学。非线性气动载荷是通过时域中的非定常带理论，利用Wagner函数的Jones近似以及跟随者气动载荷假设来计算的。此外，基于实验准静态失速曲线的平板非常规失速模型用于内插升力曲线斜率。实验和数值结果表明，镇流器位置的最小颤动速度约为 非线性气动载荷是通过时域中的非定常带理论，利用Wagner函数的Jones近似以及跟随者气动载荷假设来计算的。此外，基于实验准静态失速曲线的平板非常规失速模型用于内插升力曲线斜率。实验和数值结果表明，镇流器位置的最小颤动速度约为 非线性气动载荷是通过时域中的非定常带理论，利用Wagner函数的Jones近似以及跟随者气动载荷假设来计算的。此外，基于实验准静态失速曲线的平板非常规失速模型用于内插升力曲线斜率。实验和数值结果表明，镇流器位置的最小颤动速度约为$-5$朝向前缘的毫米。接下来，针对所测试的不同镇流器位置，获得了不同的非线性振颤后LCO行为。总而言之，模型与实验之间的良好相关性表明，本文提出的非线性建模方法能够预测经过测试的高长宽比机翼的气动弹性行为。