Self-Excited Vibration Analysis of a Rotating Cylinder Partially Filled with Liquid (Nonlinear Analysis by Shallow Water Theory)

Abstract

The self-excited whirl of an axially symmetric cylinder mounted on an elastic support system and partially filled with liquid is analyzed. Rotor unbalance, gravity, and gyroscopic terms are considered to be negligible. The whirling motion is assumed to be parallel to the axis and the liquid motion is taken as being axially uniform. In the analysis, under the assumption of a thin liquid layer, the shallow-water theory is applied to basic equations to more easily incorporate nonlinearities that exist in the surface wave of a liquid in a rotor. Applying the Galerkin method to the equations based on the shallow-water theory obtains the modal coupling equations. The harmonic balance method is applied to the modal coupling equations to obtain periodic solutions. The analytical whirl amplitudes are in good agreement with the experimental ones in previous studies under large external damping ratios. The time series analysis based on the modal coupling equations reproduces the periodic and aperiodic amplitude modulations observed in the experiment.