On Free Surface Oscillations of a Liquid Partially Filling a Rotating Cylinder : lst Report, Visualization of Resonant Mode and Analysis by Inviscid Theory

Kaneko, Shigehiko; Hayama, Shinji

doi:10.1299/jsme1958.26.1985

Cited by 4 publications

(2 citation statements)

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“…There have been a number of studies concerned with the free vibration characteristics (1)- (3) , the responses of the centrifugal wave to lateral (4), (5) and axial excitations (6) , the self-excited vibration of a system consisting of a tank and its elastic supports (7)- (13) , utilization as a dynamic absorber (14) , and the nonlinear sloshing analysis based on shallow water approximation theory (15)- (19) . These studies are classified into those which consider viscosity (5), (7)- (9), (11)- (13), (15), (16), (18) and those which use inviscid theory (1)- (4), (6), (10), (14), (17), (19) , or into those which consider the coupling with the vibrations of elastic supports (7)- (17) and those which analyze the liquid motion generated by a prescribed tank excitation (4)- (6), (18), (19) . One feature of the earlier works is that they focus on the analyses of the phenomena.…”

Section: Introductionmentioning

confidence: 99%

Study on Vibration Reduction of a Rotating Cylindrical Tank with Elastic Supports

Utsumi

2013

JSDD

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A method for reducing the vibration of a rotating cylindrical tank with elastic supports is studied by considering the case where a stationary circumferential flow relative to the tank is created by inserting rotating ring plates whose rotational speed differs from the tank's rotational speed. It is shown that the vibration can be reduced when the flow's relative velocity is negative. The relative velocity appears not only in the inertial and Coriolis terms of the Navier-Stokes equations but also in the dynamic boundary condition on the liquid surface. It is found that the vibration reduction can be caused by the relative velocity that appears in the dynamic boundary condition on the liquid surface. A semianalytical method is presented for the viscous rotating sloshing problem, for which it is customary to resort to numerical methods. The method is verified by comparing with earlier results available for the case with no stationary circumferential flow relative to the tank. This method transforms the viscous rotating sloshing problem into only several ten ordinary differential equations, thereby reducing computational efforts significantly.

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Section: Introductionmentioning

confidence: 99%

Study on Vibration Reduction of a Rotating Cylindrical Tank with Elastic Supports

Utsumi

2013

JSDD

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“…A number of investigators have investigated this phenomenon. In early stages, a number of linear analyses have been performed to investigate natural modes of the free surface wave and instability in the coupling system of the free surface wave and the rotating cylinder on an elastic support system, assuming infinitesimal disturbances (1)- (6) . In the next stage, nonlinearities in the free surface wave have been taken into account in order to predict the amplitude of the asynchronous whirl.…”

Section: Introductionmentioning

confidence: 99%

Wave Analysis of Liquid Partially Filling a Rotating Cylinder

Yoshizumi

2010

JSDD

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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 Galerkin's 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.

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