Nonlinear stability analysis of whirl flutter in a rotor-nacelle system

Abstract

Whirl flutter is an aeroelastic instability that affects propellers/rotors and the surrounding airframe structure on which they are mounted. Whirl flutter analysis gets progressively more complicated with the addition of nonlinear effects. This paper investigates the impact of nonlinear pylon stiffness on the whirl flutter stability of a basic rotor-nacelle model, compared to a baseline linear stiffness version. The use of suitable nonlinear analysis techniques to address such a nonlinear model is also demonstrated. Three types of nonlinearity were investigated in this paper: cubic softening, cubic hardening and a combined cubic softening—quintic hardening case. The investigation was conducted through a combination of eigenvalue and bifurcation analyses, supplemented by time simulations, in order to fully capture the effects of nonlinear stiffness on the dynamic behaviour of the rotor-nacelle system. The results illustrate the coexistence of stable and unstable limit cycles and equilibria for a range of parameter values in the nonlinear cases, which are not found in the linear baseline model. These branches are connected by a number of different bifurcation types: fold, pitchfork, Hopf, homoclinic and heteroclinic. The results also demonstrate the importance of nonlinear whirl flutter models and analysis methods. Of particular interest are cases where the dynamics of the nacelle are unstable despite linear analysis predicting stable behaviour. A more complete stability envelope for the combined model was generated to take account of this phenomenon.