Stochastic P-bifurcation of a 3-DOF airfoil with structural nonlinearity

In this paper, the stochastic-aeroelastic nonlinear response of a three-degree-of-freedom (3-DOF) structural nonlinear airfoil with a control flap is presented. The critical parameter conditions of stochastic P-bifurcation are solved by using the improved average method, the stochastic average method combined with the singularity theory. The results show that the periodic solution produced by Hopf bifurcation has involved a second bifurcation, the nonlinear critical speed of saddle node bifurcation points is advanced, and the airfoil appears bi-stable. The stochastic singularity analysis shows that the increasing stochastic disturbance intensity will cause a greater probability for a large amplitude stochastic flutter.