Stability analysis of a nonlinear rotating asymmetrical shaft near the resonances

作者：Shahgholi Majid; Khadem Siamak Esmaeilzadeh^*

来源：Nonlinear Dynamics, 2012, 70(2): 1311-1325.

DOI：10.1007/s11071-012-0535-7

• Parametric excitation
• Multiple scales method
• Harmonic resonance
• Bifurcation
• In-extensional effect

An asymmetrical rotating shaft with unequal mass moments of inertia and flexural rigidities in the direction of principal axes is considered. In this system, there are two excitation sources, including a harmonic excitation due to the dynamic imbalances and a parametric excitation due to shaft asymmetry. Nonlinearities are due to the in-extensionality of the shaft and large amplitude. In this study, harmonic and parametric resonances due to the mentioned effects are considered. The influences of inequality of mass moments of inertia and flexural rigidities in the direction of principal axes, inequality between two eccentricities corresponding to the principal axes and external damping on the stability and bifurcation of steady state response of the rotating asymmetrical shaft are investigated. In addition, the characteristic of stable stationary points and loci of bifurcation points as function of damping coefficient are determined. In order to analyze the resonances of the system the multiple scales method is applied to the complex form of partial differential equations of motion. The achieved results show a good agreement with those of numerical computation.

• 出版日期2012-10