On vibration behavior and motion bifurcation of a nonlinear asymmetric rotating shaft

This article investigates the nonlinear vibrations of asymmetric vertically supported Jeffcott rotor system. Asymmetry in both linear and nonlinear stiffness coefficients of the rotating shaft is considered. The disk eccentricity and its orientation angle are included in the system model. Asymptotic analysis is sought to obtain an analytical approximate solution for the considered system model in the primary resonance case. Bifurcation diagrams for the different system parameters are obtained to explore the system steady-state lateral vibrations. The main acquired results revealed that (1) the symmetric system can oscillate by one of three stable forward whirling amplitudes at the same rotational speed depending on the initial position of the rotating disk. (2) Asymmetry in the linear stiffness coefficient does not affect the symmetry of the whirling motion, but it may change the system natural frequency. (3) Asymmetry in the nonlinear stiffness coefficient is responsible for both asymmetrical and backward whirling motions. All obtained analytical results have been verified via solving the system original equations numerically, where the analytical and numerical results are in excellent agreement.