Dynamics of flexible rotors partially filled with a viscous incompressible fluid

A linear theory is developed to study the motion of a hollow circular cylinder rotating with constant angular velocity and partially filled with a viscous incompressible fluid. Many different rotor models can be studied using this analysis.
A two-dimensional theory which ignores axial motion in the fluid is discussed first. This theory exhibits all of the essential features of liquid-rotor coupling and is used to analyze a simple rotor configuration and explore the ramifications of the analysis. The full three-dimensional theory is then developed and used to analyze more complicated rotors.
The results of this analysis predict that over a range of operating speeds, the rotor-fluid system is unstable. The extent of this unstable region is determined by the system parameters. The interplay between the viscosity of the fluid and damping on the rotor is especially important in determining stability boundaries.