In this paper 1/2 subharmonic resonance under parametric excitation in a rotating shaft with an unsymmetrical stiffness is studied. 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 rotating coordinate system into stationary coordinate system and introducing a complex variable we obtain the motion equation in complex variable forms in which the stiffness coefficient varies periodically as time. By applying the method of multiple scales we obtain the averaged equation and the amplitude-frequency response equation. Via the theory of singularity we analyze the stability of the steady-state solutions. This study exhibits that the shaft with unsymmetrical stiffness possess an unstable range in neighborhood of the rotating speed. The asymmetry and the external damping have great influence on stability of the shaft.
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