The stability of an elastically supported rotor spinning with constant angular velocity is studied. The rotor has a cavity of arbitrary meridian and is partially filled with an ideal fluid. The motions of the system are governed by linearized equilibrium conditions for the rotor and field equations as well as boundary conditions for the fluid. Due to the arbitrary shape of the meridian, it is not possible to solve the boundary value problem in closed form. Therefore a variational expression is developed which satisfies the boundary conditions naturally. The variational problem is solved approximately by the finite element method. The results, incorporated in the equilibrium conditions for the rotor, lead to stability statements. For numerical and experimental investigations, two rotors, one with an elliptical and one with a conical cavity are used. The fill medium is water. There is a close correlation between numerical and experimental results.

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