Primary resonances of a nonlinear in-extensional rotating shaft

In this paper, primary resonances of a simply supported in-extensional rotating shaft with large amplitudes are studied. The method of multiple scales is applied to the discretized equations as well as to the complex form of partial differential equations of motion. The effects of diametrical mass moment of inertia, eccentricity and external damping are investigated on the steady state response of the rotating shaft. The loci of saddle node bifurcation points are plotted as functions of damping coefficient and eccentricity.