Combination Resonance of Nonlinear Rotating Balanced Shafts Subjected to Periodic Axial Load

Dynamic behavior of a circular shaft with geometrical nonlinearity and constant spin, subjected to periodic axial load is investigated. The case of parametric combination resonance is studied. Extension of shaft center line is the source of nonlinearity. The shaft has gyroscopic effect and rotary inertia but shear deformation is neglected. The equations of motion are derived by extended Hamilton principle and discretized by Galerkin method. The multiple scales method is applied to the complex form of equation of motion and the system under parametric combination resonance is analyzed. The attention is paid to analyze the effect of various system parameters on the shape of resonance curves and amplitude of system response. Furthermore, the role of external damping on combination resonance of linear and nonlinear systems is discussed. It will be shown that the external damping has different role in linear and nonlinear shaft models. To validate the perturbation results, numerical simulation is used.