Robust flutter analysis of an airfoil with flap freeplay uncertainty

Modern robust flutter method is an advanced technique for flutter margin estimation. It always gives the worst-case flutter speed with respect to potential modeling errors. Most literatures are focused on linear parameter uncertainty in mass, stiffness and damping parameters, etc. But the uncertainties of some structural nonlinear parameters, the freeplay in control surface for example, have not been taken into account. A robust flutter analysis approach in μ-framework with uncertain nonlinear operator is proposed in this study. Using describing function method the equivalent stiffness formulation is derived for a two dimensional wing model with freeplay nonlinearity in its flap rotating stiffness. The robust flutter margin is calculated for the two dimensional wing with flap freeplay uncertainty and the results are compared with that obtained with nominal parameter values. It is found that by considering the perturbation of freeplay parameter more conservative flutter boundary can be obtained, and the proposed method μ-framework can be applied in flutter analysis with other types of concentrated nonlinearities.