Self-excited vibrations of the variable mass rotor/fluid system

In this paper the variable mass rotor/fluid system is considered. A rotor with variable mass is settled in hydrodynamic bearings. The dynamic properties of the rotor on which the fluid force and the impact force (due to mass variation) act are analyzed. The conditions of stable rotation are obtained applying the direct Lyapunov theorem. The self-excited vibrations are determined analytically. The Krylov-Bogolubov method is extended for solving the second order differential equation with a complex deflection function, small non-linearity and time variable parameters and a significant damping term. Analyzing the amplitude of self-excited vibrations, the conditions of unstable motion are defined. Special attention is given to the effect of interactive influence of the inertial fluid force and the impact force on the stability of rotation of the rotor. For the rotor on which the band winds up, the vibrations are obtained analytically. The results are compared with numerical ones. (C) 1998 Academic Press Limited.