Forced vibrations analysis of a rotating shaft with considering the nonlinear geometric and inertia terms and the gyroscopic effect

Abstract This paper has been devoted to the importance of considering the effects of nonlinear geometric and inertia terms and the effect of gyroscopic term on the forced vibrations of an unbalance rotating shaft. The nonlinear partial differential equations have been derived by using the extended Hamilton's principle and have been transformed to the ordinary differential equations by using the Galerkin method. Then the method of multiple scales has been applied to the discretized ordinary differential equations and the modulation equations describing interaction between modes have been obtained. By applying the solvability condition on the resulting modulation equations and considering the stable conditions in the vibration analysis, the frequency response diagrams have been plotted. The effect of the gyroscopic term, nonlinear geometric and inertia terms have been presented in the frequency response diagrams. In plotting the frequency response diagrams of rotating shaft, its rotating speed has been considered very close to the shaft’s forward natural frequency. Numerical results showed that the hardening type behavior has been observed in simulations due to nonlinear terms.