Combination resonances in a rotating shaft

Using the method of harmonic balance, combination resonances of in-extensional simply supported rotating shafts with nonlinearities in curvature and inertia are studied. The frequency–response curves are plotted for the first two modes. The effects of mass moment of inertia, eccentricity and external damping coefficient 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. Results of perturbation method are validated with numerical simulations.