This paper investigates the effect of model uncertainty on the nonlinear dynamics of a generic aeroelastic system. Among the most dangerous phenomena to which these systems are prone, Limit Cycle Oscillations are periodic isolated responses triggered by the nonlinear interactions among elastic deformations, inertial forces, and aerodynamic actions. In a dynamical systems setting, these responses typically emanate from Hopf bifurcation points, and thus a recently proposed framework, which address the problem of robustness from a nonlinear dynamics viewpoint, is employed. Briefly, the notion of robust bifurcation margin extends the concept of \(\mu \) analysis technique from the robust control theory. The main contribution of this article is a systematic investigation of the numerous scenarios arising in the study of nonlinear flutter when uncertainties in the model are accounted for in the analyses. The advantages of adopting this framework include the possibility to: quantify relevant information for the determination of the nonlinear stability envelope; gain a more in-depth understanding of the physical mechanisms triggering subcritical and supercritical Hopf bifurcations; and reveal properties of the nominal system by identifying isolated branches not straightforward to detect with conventional numerical approaches.

本文研究了模型不确定性对通用气动弹性系统非线性动力学的影响。在这些系统最容易发生的最危险现象中，极限循环振荡是由弹性变形，惯性力和空气动力作用之间的非线性相互作用触发的周期性孤立响应。在动力学系统设置中，这些响应通常从Hopf分叉点发出，因此采用了最近提出的框架，该框架从非线性动力学的角度解决了鲁棒性问题。简而言之，稳健的分叉余量的概念扩展了\（\ mu \）的概念鲁棒控制理论的分析技术。本文的主要贡献是当分析中考虑了模型的不确定性时，系统地研究了非线性颤动研究中出现的多种情况。采用此框架的优点包括：量化相关信息以确定非线性稳定性包络的可能性；对触发亚临界和超临界Hopf分支的物理机制有更深入的了解；并通过识别孤立的分支来揭示名义系统的特性，这些分支不是用常规数值方法即可直接检测到的。