Center manifold reduction for the flutter of airfoils with gust loading

An analysis of the classic binary airfoil system perturbed by a vertical gust is presented in this paper. To simplify the derivation, the gust disturbance is replaced with white noise, and a quasi-steady aerodynamic force is used to model the aerodynamic loading. Random bifurcation in this dynamical system is studied using the ideas of center-manifold reduction, normal form and the polar coordinates transformation. Then, an explicit presentation for the stationary probability density function is found as an approximate analytical solution to the related Fokker–Planck equation. From the results, we conclude that the P-bifurcation point will not produce qualitative changes, while the D-bifurcation point will disappear under a vertical gust.