Bifurcation Analysis for a Simple Dual-Rotor System with Nonlinear Intershaft Bearing Based on the Singularity Method

This paper aims to classify bifurcation modes for two interrelated primary resonances of a simple dual-rotor system under double frequency excitations. The four degree-of-freedom (4DOF) dynamic equations of the system considering the nonlinearity of the intershaft bearing can be obtained by using the assumed mode method (AMM) and Lagrange’s equation. A simplified method for dynamic equations is developed due to the symmetry of rotors, based on which the amplitude frequency equations for two interrelated primary resonances are obtained by using the multiple scales method. Furthermore, the validity of the simplified method for dynamic equations and the amplitude frequency equations solved by the multiple scales method are confirmed by numerical verification. Afterwards, the bifurcation analysis for two interrelated primary resonances is carried out according to the two-state-variable singularity method. There exist a total of three different types of bifurcation modes because of double frequency excitations of the dual-rotor system and the nonlinearity of the intershaft bearing. The second primary resonance is more prone to have nonlinear dynamic characteristics than the first primary resonance. This discovery indicates that two interrelated primary resonances of the dual-rotor system may have different bifurcation modes under the same dynamic parameters