Vibrations in fluid-filled rotor and the gyroscopic effect

The vibrational behavior of a hollow cylindrical container partially filled with an ideal fluid is analytically and experimentally investigated. The container's movement makes it function as a rotor while the liquid acts as a continuum in three-dimensional vibration. The coupled vibrations of rotor and continuum are discussed in terms of initial equations which are expressed in the moving, rotor-bound reference system via Eulerian hydrodynamic equations. The equations are converted into an eigenvalue problem which is composed of the boundary value problem for the liquid and the system of container equations. The characteristic equation of the eigenvalue problem is set up and stability predictions are made. Above a critical rotational speed which is dependent on the volume of fluid, a broad region of unstable rotor vibrations is found to exist. These vibrations arise on the free surface of the rotating fluid ring and act in the sense opposite to the rotation. Experimental results were in excellent agreement with calculations and showed that increasing fluid viscosity lowered the critical value.