On the stability of steady rotation of a cylinder partly filled with a viscous incompressible fluid

Derendiaev, N. V.; Sandalov, Vladimir M.

doi:10.1016/0021-8928(82)90030-2

Cited by 8 publications

(5 citation statements)

References 1 publication

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“…The stability of a rotor is partially filled with a viscous, incompressible fluid, the angular velocity of which is kept constant by means of a special drive, was considered earlier in [2]. The cavity of the rotor has the shape of a tall cylinder.…”

Section: A Rotor Partially Filled With a Fluidmentioning

confidence: 99%

“…After some reduction, the solution of the linearized problem of the plane-parallel motion of the fluid accompanying the angular precession of the rotor [2] can be represented in the form…”

Section: A Rotor Partially Filled With a Fluidmentioning

confidence: 99%

“…The stability of a rotor, partially filled with a fluid, was investigated in [2], subject to the condition that the angular velocity of rotation is constant, and the boundaries of domains with a different degree of instability were constructed in the parameter space of the problem. The difficulties of investigating distributed models have prompted an analysis of the possibility of constructing discrete models [3], which could describe some important features of the behaviour of a rotor system containing a fluid with satisfactory accuracy.…”

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confidence: 99%

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The stability of the steady motions of a rotor system with a fluid using a discrete model

Derendyayev¹,

Солдатов²

2004

Journal of Applied Mathematics and Mechanics

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Section: A Rotor Partially Filled With a Fluidmentioning

confidence: 99%

“…After some reduction, the solution of the linearized problem of the plane-parallel motion of the fluid accompanying the angular precession of the rotor [2] can be represented in the form…”

Section: A Rotor Partially Filled With a Fluidmentioning

confidence: 99%

mentioning

confidence: 99%

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The stability of the steady motions of a rotor system with a fluid using a discrete model

Derendyayev¹,

Солдатов²

2004

Journal of Applied Mathematics and Mechanics

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“…Yukio Ishida et al applied a method, which utilizes discontinuous spring characteristics, to suppress unstable vibrations in an asymmetrical rotor system, an asymmetrical shaft system, and a rotor system partially filled with liquid [18]. N. V. Derendyaev et al investigated the stability of a cylinder filled with different kinds of liquid, including viscous incompressible liquid, a stratified viscous incompressible liquid and a stratified non-uniform viscous incompressible liquid [19][20][21][22]. In 1988, Derendyaev proved that Andronov-Hopf bifurcations may occur in a rotor system filled with liquid [23].…”

Section: Introductionmentioning

confidence: 99%

An analytical investigation on the dynamic stability of a rotor filled with liquid

Li¹,

Wang²,

Yuan³

2018

J. vibroeng.

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This paper deals with the dynamic stability of a rigid rotor arbitrarily filled with liquid. On the basis of the established coupled-field equations of the rotor system, the general whirling eigenequation, which is a quartic complex coefficients equation, is derived. In order to obtain the solutions of the general whirling eigenequation, a mathematical method is proposed. To illustrate the precision of calculating results, a comparison is carried out between the present analysis and the numerical results. The results show that two calculation results are in good agreement. Then the stability of the rotor system is analyzed. It is shown that the dynamic instability occurs at a particular bound of the spinning speed. Moreover, the effects of system parameters, such as fluid-fill ratio and mass ratio, on the unstable regions are discussed.

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“…The resonant excitation of waves in a fluid in the rotor chamber is the main cause of instability of stationary rotation of rotor systems [1,2]. Currently, systems are used in which the influence of gravity is negligible compared to the influence of the centrifugal and Coriolis forces.…”

Section: Introductionmentioning

confidence: 99%

Magnetic field effect on waves in a centrifuged layer of a rotating conducting viscous fluid

Klueva

Sandalov

Tkach

et al. 2015

J Appl Mech Tech Phy

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This paper considers wave processes in a centrifuged layer of an incompressible viscous conducting fluid in an axial magnetic field in the cavity of a rapidly rotating infinite cylinder with insulating walls. Inertial modes (solutions of the linearized boundary-value problem of magnetohydrodynamics) are represented as a superposition of helical fields. Expressions for the vorticity parameters of the helical flows forming the inertial mode at a small Stewart number are given. Dispersion curves of inertial waves are constructed, and the influence of the magnetic field on the flow field is analyzed. The critical frequencies at which the lowest (surface) mode arises are determined. The spatial and temporal stability of the modes are investigated.

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On the stability of steady rotation of a cylinder partly filled with a viscous incompressible fluid

Cited by 8 publications

References 1 publication

The stability of the steady motions of a rotor system with a fluid using a discrete model

The stability of the steady motions of a rotor system with a fluid using a discrete model

An analytical investigation on the dynamic stability of a rotor filled with liquid

Magnetic field effect on waves in a centrifuged layer of a rotating conducting viscous fluid

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