The dynamic behavior of a flexible rotor system with nonlinear support was studied by the numerical method of a model and the solution combining the finite element model with nonlinear supports. The finite element method (FEM) was used to build the model of the rotating shaft and the rotary table

and the matrix was used for combination; the discrete element method was used to model the support (including: rolling bearing and squeeze film damper (SFD))

which specifically consists of four elements: bearing inner ring

outer ring

SFD inner ring and supporting cage. The finite element part and the discrete element part were connected by the nodes at the shaft end

and the displacement at the shaft end was transmitted to the nonlinear support. The nonlinear force and the nonlinear support calculated by the displacement at the support acted on the finite element rotor part at the shaft end in turn. In order to solve the coupling problem of the finite element rotor and the nonlinear support

a comprehensive iterative method was proposed to overcome the limitation of the traditional finite element method for solving the implicit nonlinear support at the shaft end. Because the Timoshenko beam element was used to model the rotating shaft

the gyroscopic moment and the flexibility of the shaft can be considered

which can better reflect the real effect of nonlinear support on the vibration.In the 20 shaft finite elements rotor model

the nonlinear response was more reflected in the 1 and 21 nodes closed to the nonlinear supports

and the nodes near the shaft end in the response spectrum can reflect two times and three times the flexible vibration frequency of the rolling bearing.