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

Yoshizumi, Fumitaka

doi:10.1299/kikaic.73.1338

Cited by 3 publications

(9 citation statements)

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“…The equation set for the liquid motion obtained in the first report (12) is coupled with the equation of the rotor motion.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…(4) - (6) to the basic equations of Eqs. (1) -(3) yields the one-dimensional equation along the circumference as follows (12) :…”

Section: Shallow-water Approximationmentioning

confidence: 99%

“…(12). The form proposed by Chester (19) is applied to the wall-friction term, which is the second to last term on the right-hand side of Eq.…”

Section: Shallow-water Approximationmentioning

confidence: 99%

“…(2) between y and h (12) . The Fourier coefficient of the friction stress f for the component of sinnθ is expressed as the term with F rn in Eq.…”

Section: Shallow-water Approximationmentioning

confidence: 99%

“…In the first report (12) , a nonlinear formulation that incorporates the nonlinear terms neglected in the previous study (6) has been proposed in order to predict the fluid force that acts on the rotating cylinder forced to undergo a harmonic whirl motion. The formulation is derived by applying the shallow-water approximation to the basic equations to more easily incorporate nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

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

Yoshizumi

2011

JSDD

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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.

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“…The equation set for the liquid motion obtained in the first report (12) is coupled with the equation of the rotor motion.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…(4) - (6) to the basic equations of Eqs. (1) -(3) yields the one-dimensional equation along the circumference as follows (12) :…”

Section: Shallow-water Approximationmentioning

confidence: 99%

“…(12). The form proposed by Chester (19) is applied to the wall-friction term, which is the second to last term on the right-hand side of Eq.…”

Section: Shallow-water Approximationmentioning

confidence: 99%

“…(2) between y and h (12) . The Fourier coefficient of the friction stress f for the component of sinnθ is expressed as the term with F rn in Eq.…”

Section: Shallow-water Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Yoshizumi

2011

JSDD

Self Cite

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Vibrations in Rotary Machines

2014

Flow-Induced Vibrations

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The unbalanced rotating cylinder partially filled with fluid; multiple scales analysis of a forced Korteweg-de Vries-Burgers equation

Langthjem

Imura

Yamaguchi

2022

Preprint

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The paper is concerned with an unbalanced cylindrical rotor containing a small amount of fluid, spun out to form a thin fluid layer on the inner surface of the cylinder. The main interest is in the possibility of this fluid layer to counterbalance an unbalanced point mass, as well as in the derivation of approximate analytical solutions to the non-linear, forced equation that governs the fluid layer thickness perturbation. This equation is of the forced Korteveg-de Vries-Burgers type, and the analysis is based on the method of multiple scales. The leading-order solutions are capable of giving a qualitative explanation of the balancing effect of the fluid, in other words, to explain the mechanics of the so-called `fluid balancer'. Additionally, good agreement between theoretical and experimental results is found.

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

Cited by 3 publications

References 0 publications

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

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

Vibrations in Rotary Machines

The unbalanced rotating cylinder partially filled with fluid; multiple scales analysis of a forced Korteweg-de Vries-Burgers equation

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