The dynamic response of a thin buckled panel in a supersonic wind-tunnel experiment is investigated. Measured time histories of the panel displacement and velocity show co-existing, nonlinear responses with features of periodic and chaotic oscillations. Fully coupled computational analyses are conducted in order to study and interpret the aeroelastic phenomena observed during the experiments. A computationally efficient modeling framework is formulated with a nonlinear structural reduced-order model and enriched piston theory aerodynamics for the mean flow. The simulations predict the onset of the chaotic motions observed in the experiments, albeit with an approximately 21% increase in the oscillation amplitude. A linearized equation governing the distance between neighboring solutions is derived and used to compute the largest Lyapunov exponent in order to prove the existence of chaos. A modified Riks analysis highlights the co-existence of multiple equilibrium positions which predisposes the nonlinear system to chaos. The system’s sensitivity to cavity pressure, temperature differential, and initial conditions is also investigated. Variation of the cavity pressure and temperature differential yields additional regions of dynamic activity that were not explored during the experiments.

研究了超音速风洞实验中薄屈曲面板的动态响应。面板位移和速度的测量时间历程显示共存的非线性响应具有周期性和混沌振荡的特征。进行了完全耦合的计算分析，以研究和解释实验期间观察到的气动弹性现象。计算高效的建模框架由非线性结构降阶模型和用于平均流的丰富活塞理论空气动力学组成。模拟预测了实验中观察到的混沌运动的开始，尽管振荡幅度增加了大约 21%。导出控制相邻解之间距离的线性方程，并用于计算最大的李雅普诺夫指数，以证明混沌的存在。修改后的 Riks 分析强调了多个平衡位置的共存，这使非线性系统易于混沌。还研究了系统对腔压力、温差和初始条件的敏感性。腔压力和温差的变化产生了在实验期间未探索的额外动态活动区域。并且还研究了初始条件。腔压力和温差的变化产生了在实验期间未探索的额外动态活动区域。并且还研究了初始条件。腔压力和温差的变化产生了在实验期间未探索的额外动态活动区域。