Modal characteristics and dynamic stability of a whirling rotor with flexible blades

This paper analyses the modal characteristics and dynamic stability of a whirling rotor with flexible blades. A rigid disk with flexible blades, which is called a rotor-blade system in this paper, is modelled as a Jeffcott rotor with Euler-Bernoulli beams. From the nonlinear equations of motion, we derived the equilibrium position and the linearized equations around the equilibrium position by the perturbation method. Based on the linearized equations, a modal analysis was performed for the variations of the supporting stiffness and rotating speed. Furthermore, we investigated the effects of the whirling motion on the natural frequencies and mode shapes and found the threshold speed of instability that cause instability in the system. In addition, we also studied the characteristics of stable and unstable regions in terms of the rotating speed and the supporting stiffness.