On the effect of model uncertainty on the Hopf bifurcation of aeroelastic systems

Abstract

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 $$\mu $$ μ 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.

Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview

“…Stochasticity quantification is of extreme significance and the key step to subsequent research studies and has attracted much attention from scholars in the aeroelastic fields. 66,[86][87][88][89][90][91] It should be emphasized that appropriate models to quantify the uncertainties are of considerable importance to flutter analysis of the aeroelastic systems. In general, probabilistic, non-probabilistic, and fuzzy methods are three main approaches employed for modeling different uncertainties.…”

“…Riley et al 88 proposed a methodology for uncertainty quantification in an aeroelastic airfoil model, and the modeling uncertainty was used to drive the necessity of further experimental data points. More recently, Iannelli et al 91 explored the influences of model uncertainty on the nonlinear dynamics of an aeroelastic system. Besides, Zheng and Qiu 105 proposed a novel numerical method to study the flutter stability of airfoil systems with interval uncertain parameters.…”

Numerical study on the nonlinear characteristics of shock induced two-dimensional panel flutter in inviscid flow

“…In the studies mentioned above, the subcritical bifurcation characteristics of the shock induced panel flutter were observed in both the inviscid and viscous flow [9,10,25]. As the subcritical bifurcation tends to be more dangerous than supercritical bifurcation in engineering [30][31][32][33], understanding the system bifurcation behavior is of great importance in the aircraft structural design. Visbal [9] noted that increasing the shock strength can drive the system transition from a subcritical bifurcation to a supercritical bifurcation.…”