Stability analysis of a spinning shaft in the concentric cylinder filled with an incompressible fluid

This paper deals with the stability of a spinning shaft in a concentric cylinder filled with an incompressible fluid. The steady-state momentum and continuity equations for the ex-ternal fluid are established. Using Taylor expansion, the fluid forces exerted on the shaft are calculated. The shaft is in the Rayleigh model taking into account the rotary inertia and gyroscopic effects. Accordingly, the governing equation of the considered system is formulated analytically. The explicit characteristic frequency equation for the pinned-pinned spinning shaft system is then derived. Finally, the stability of the system is studied by means of characteristic value analysis.