Method of multiple scales for vibration analysis of rotor-shaft systems with non-linear bearing pedestal model

The method of multiple scales is developed to analyze the free and forced vibration of non-linear rotor-bearing systems. The rotating shaft is described by the Timoshenko beam theory which considers the effect of the rotary inertia and shear deformation. A non-linear bearing pedestal model is assumed which has a non-linear spring and linear damping characteristics. Numerical simulations are carried out to illustrate the non-linear effect on the free and forced vibrations of the system. It is shown that for free vibrations, the amplitude has a one-to-one relationship with the non-linear natural frequency. For steady-state response, however, multi-valued displacements occur, indicating the existence of bifurcation points in the system.