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.

The Inertial Disturbances of Fluid Movement in the Chamber of a Liquid Autobalancer

“…Berman A. et al [41] applied numerical analysis and an experiment focusing on the case of asynchronous precession, and found that nonlinear surface waves can exist on the liquid layer in the form of relatively weak hydraulic jumps with waves generated by it. Similar studies by Chato D. and Dalton P. [42] and Yoshizumi F. [43] are purely experimental and numerical.…”

“…Berman A. et al [41], Chato D. and Dalton P. [42] and Yoshizumi F. [43] used nonlinear models. Berman A. et al [41] applied numerical analysis and an experiment focusing on the case of asynchronous precession, and found that nonlinear surface waves can exist on the liquid layer in the form of relatively weak hydraulic jumps with waves generated by it.…”

Vibration analysis of a cylindrical rotor containing liquid with stationary circumferential flow

“…A feature of this research area is that in order to explain experimentally observed stable vibration, nonlinear analyses based on the shallow water approximation were conducted (Berman et al, 1985;Cheng et al, 1985;Colding-Jorgensen, 1993;Jinnouchi et al, 1985;Yoshizumi, 2011;Kasahara et al, 2000). However, no study has been conducted on semianalytical methods that allow for arbitrary liquid depth and all kinds of nonlinearity in the governing equations for the rotating viscous liquid, and that examine what kind of nonlinearity causes the transition from unstable response to stable vibration.…”