Stability and bifurcation analysis for an airfoil model with a high-order nonlinear spring

In this paper, the stability and bifurcation of an airfoil model with a high-order nonlinear spring are investigated both analytically and numerically. Two possible types of bifurcation at the equilibrium point are studied. It is proved that the zero characteristic root can only be a single zero. With the help of the center manifold theory and the normal form theory, the expressions of critical bifurcation curves leading to initial bifurcation and secondary bifurcation are obtained. Numerical simulations confirm the theoretical results.