In order to improve efficiency, the gas and steam turbine cycle technology, represented by newly distributed rod fastening rotor system, gets fast development in electrical production departments. In this paper, nonlinear characteristics of the distributed rod fastening system are studied by a novel torsional vibration model. By using equivalent and simplification method, torsional vibration model of the distributed rod fastening rotor system are established. Based on the average method, analytical solutions and the amplitude frequency curves of the dynamic system are obtained. Further, the stability of periodic solutions of the dynamic system is studied, and impacts of the external excitation, damping and cubic stiffness are investigated respectively. Analysis results of the dynamic system have a guiding significance to design.