Equivalent linearization method for the flutter system of an airfoil with multiple nonlinearities

The equivalent linearization method (ELM) was extended to analyze the flutter system of an airfoil with multiple nonlinearities. By replacing the cubic plunging and pitching stiffnesses by equivalent quantities, linearized equations for the nonlinear system were deduced. According to the linearized equations, approximate solutions for limit cycle oscillations (LCOs) were obtained in good agreement with numerical results. The influences of the linear and cubic stiffnesses on LCOs were analyzed in detail. Reducing linear pitching stiffness leads to decreasing of the critical flutter speed. For linear plunging stiffness, the opposite is true. Also, it reveals that the bifurcation could be supercritical or subcritical, which is related to the ratio between the coefficient of cubic pitching stiffness and that of plunging one.