Numerical Continuation of Limit Cycle Oscillations and Bifurcations in High-Aspect-Ratio Wings

Abstract

This paper applies numerical continuation techniques to a nonlinear aeroelastic model of a highly flexible, high-aspect-ratio wing. Using continuation, it is shown that subcritical limit cycle oscillations, which are highly undesirable phenomena previously observed in numerical and experimental studies, can exist due to geometric nonlinearity alone, without need for nonlinear or even unsteady aerodynamics. A fully nonlinear, reduced-order beam model is combined with strip theory and one-parameter continuation is used to directly obtain equilibria and periodic solutions for varying airspeeds. The two-parameter continuation of specific bifurcations (i.e., Hopf points and periodic folds) reveals the sensitivity of these complex dynamics to variations in out-of-plane, in-plane and torsional stiffness and a ‘wash out’ stiffness coupling parameter. Overall, this paper demonstrates the applicability of continuation to nonlinear aeroelastic analysis and shows that complex dynamical phenomena, which cannot be obtained by linear methods or numerical integration, readily exist in this type of system due to geometric nonlinearity.

Keywords

• nonlinear dynamics
• flutter
• aeroelasticity
• numerical continuation
• high-aspect-ratio wing
• Hopf bifurcation
• periodic fold bifurcation