Nonlinear vibration and stability analysis of a dual-disk rotor-bearing system under multiple frequency excitations

This paper aims to investigate the nonlinear vibration characteristics and stability of a dual-disk rotor-bearing system under multi-frequency excitations. A 4-degree-of-freedom dynamic model is established using the assumed mode method, considering the bearing’s cubic nonlinearity. The system is solved using the multiple scale method combined with arc-length continuation. The stability of the system’s solutions is determined by solving the eigenvalues of the Jacobian matrix of the averaged equations. The nonlinear vibration characteristics and stability of the dual-disk rotor system under simultaneous resonance conditions are obtained. The results show that changes in system parameters can lead to Saddle-Node and Hopf bifurcations, as well as the occurrence of multi-valued solutions and symmetry-breaking phenomena. Additionally, simultaneous resonance leads to interaction between the two modes, where the relative positions of the resonance peaks of these modes influence the system’s dynamic behavior. Variations in system parameters can alter the relative positions of resonance peaks, leading to more complex effects on nonlinear responses. This research provides significant insights into the dynamic behavior of the dual-disk rotor-bearing system under multi-frequency excitations, which is meaningful for designing and optimizing rotor systems.