Analytical model for nonlinear vibration of flexible rotor system

An analytical model is proposed to analyze a series of typical nonlinear behaviors of flexible rotor system, such as resonance, oscillation, whirl and whip. The model is constructed by introducing a defined nonlinear scale factor epsilon, nonlinear stiffness and nonlinear damping. Based on multi-scale method, the analytical solutions of steady-state and transient-state are derived, and the nonlinear natural frequency and Frequency Response Equation (FRE) are obtained. A transient time scale factor t(1) is defined to reflect the transient-state influence on steady-state solution. The experimental result also verifies the rationality and validity of the analytical model and the analytical solutions.