Internal, combinational and sub-harmonic resonances of a nonlinear asymmetrical rotating shaft

The internal, combinational and sub-harmonic resonances of a simply supported rotating asymmetrical shaft with unequal mass moments of inertia and bending stiffness in the direction of principal axes are simultaneously considered. The excitation terms are due to dynamic imbalances of shaft and shaft asymmetry. The nonlinearities are due to extensionality of shaft and large amplitudes. To analyze the nonlinear equations of motion, the method of harmonic balance is utilized. The influences of inequality between two eccentricities corresponding to the principal axes and external damping on the steady-state responses and bifurcation points of the asymmetrical rotating shaft are investigated. The numerical computations are utilized to verify the harmonic balance method results. The results of harmonic balance method are in accordance with those of numerical computations.