Local bifurcation analysis of a rotating blade

• The stability and bifurcation behaviors of the rotating blade are proposed.
• Norm form is obtained through a systematic and efficient computation method.
• Hopf bifurcation may occur in the rotating blade.
• Stability conditions of the steady state solutions are determined.
• Numerical solutions are obtained, which agree with the analytical results.

In this paper, the stability and local bifurcation for the rotating blade under high-temperature supersonic gas flow are investigated using analytical and numerical methods. Based on obtained four-dimensional averaged equation for the case of 1:1 internal resonance and primary resonance, two types of critical points for the bifurcation response equations are considered. The points are characterized by a double zero and two negative eigenvalues and two pairs of purely imaginary eigenvalues, respectively. For each type,the steady state solutions and the stability region is obtained with the aid of center manifold theory and normal form theory. We find the Hopf bifurcation solution which indicates the blade will flutter. In summary, the numerical solutions, whose initial conditions are chosen in the stability region, agree with the analytic results.