Dynamics and stability analysis of an axially functionally graded hollow rotor partially filled with liquid

The dynamics and stability of an axially functionally graded (AFG) hollow rotor partially filled with liquid are performed in this paper. Based on the Euler-Bernoulli beam theory, the governing equation of transverse vibration of an AFG liquid-filled rotor is derived using Hamilton principle. For the exponentially graded liquid-filled rotor with simply supports, the exact whirl frequency equation and the stability prediction model are obtained analytically. The validity of the present analysis is demonstrated by comparing with the existing data in the literature. Using the obtained analytical models, the effects of parameters including gradient parameter, mass ratio and cavity ratio on the whirl speed, critical spinning speed and system stability are put into evidence through a set of parametric studies. The results show that these parameters play an important role in the whirl speed and stability of the rotor system. Furthermore, the obtained results also indicate that the critical spinning speed of an AFG liquid-filled rotor is strongly dependent on the mass ratio and gradient parameter.