Dynamic characteristics of a open crack in hollow shaft rotor system was investigated. By using the finite element method

the equations of motion were formulated

where the weight and the unbalanced excitation were considered and the stiffness matrix was derived with the consideration of the time-varying of the neutral axis in the crack element cross-section. By using the harmonic balance method

the equations were solved approximately and analyzed numerically. The three-dimensional amplitude-frequency curves of different crack depth were obtained to indicate that the vertical response peaks were presented at critical rotating speeds and the subcritical rotating speeds. The varying of the critical rotating speed versus different depths and different locations of the crack was analyzed to obtain that the deeper crack which located near the disc with a larger inertia parameter made a greater impact on the system

and the critical rotating speed decrease quick. The nonlinear responses of the system at the subcirtical rotating speeds were investigated respectively

where the super-harmonic resonances were shown correspondingly. The proposed modeling method of the hollow shaft crack provides a theoretical guidance for nonlinear dynamic studying the aero-engine rotor systems with crack faults.