Abstract: The parametrical resonance and stability in a rotating shaft with an asymmetrical stiffness is analyzed. By means of the Hamilton’s principle the nonlinear differential equations of motion of the shaft are derived in the rotating coordinate system. Transforming the equations of motion from rotting coordinate system into stationary coordinate system and introducing a complex variable, the motion equation in complex variable forms in which the stiffness coefficient vnries periodically as time, is obtained. By applying the method of averaging, the averaged equation and the amplitude-frequency response equation are obtained. According to the theory of singularity, the stability and bifurcation of the steady-state solutions are analyzed.

Key words: Bifurcation, Method of averaging, Parametrical resonance, Shaft with unsymmetrical stiffness, Stability