Wave Analysis of Liquid Partially Filling a Rotating Cylinder : (Nonlinear Resonance Curve by Shallow Water Theory)

概要

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Wave motion of a liquid in a rotating, axially symmetric container undergoing a whirl motion is investigated. In the analysis of the present study, gravity is considered to be negligible and the liquid motion is taken as being axially uniform. Assuming that the liquid layer is thin, based on the shallow-water theory, the equations of motion are simplified to a one-dimensional problem along the circumference of the container. The modal coupling equations that include the nonlinear effects of the wave motion are obtained by applying Galerkins method. Periodical solutions under harmonic whirl motion, which give resonance curves, are determined by applying the harmonic balance method to the modal coupling equations. The wave height and the fluid force acting on the container obtained from the analysis are compared with experimental results reported in previous studies. Good agreement is observed between the results of the present analysis and the experimental results with respect to the wave height profile and the magnitude of the fluid force by which the asynchronous whirl motion of the container is excited.