Bifurcation analysis for 2:1 and 3:1 super-harmonic resonances of an aircraft cracked rotor system due to maneuver load

This paper focuses on the local bifurcation characteristics of an aircraft cracked rotor system mainly for the 2:1 and 3:1 super-harmonic resonances induced by the maneuver load. The motion equations of the system are formulated with the consideration of the nonlinear stiffness of the Duffing type and the breathing of a transverse crack on the shaft, as well as the maneuver load induced by the climbing and diving flight of the aircraft. By using the multiple scales method, the motion equations are analytically solved to obtain the bifurcation equations for 2:1 and 3:1 super-harmonic resonances, respectively. Furthermore, the two-state variable singularity method is employed to analyze the local bifurcation characteristics of the system affected by crack coefficient and maneuver load. For each case, two curves of hysteresis set dividing K-G parameter plane into three regions are demonstrated. Accordingly, bifurcation modes for different parameter combinations from the three regions and the two curves are obtained. The approach in this paper will provide an effective and convenient way to analyze the bifurcation characteristics of dynamical systems. The results in this paper will contribute to a better understanding of the effect of the maneuver load on the response and bifurcation characteristics of aircraft cracked rotor systems.