Investigation of the interaction between a viscous incompressible fluid layer and walls of a channel formed by coaxial vibrating discs

Mogilevich, L. I.; Popov, V. S.

doi:10.1134/s0015462811030033

Cited by 25 publications

(16 citation statements)

References 2 publications

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“…The bound hydroelasticity problem is solved in the undimensional variables (1) -(6) by perturbation method [12][13][14][15] with the use of two small parameters describing the relative width of liquid layer and relative outer elastic geometrically irregular shell sagging by presupposing the harmonic law of pressure pulsation liquid. Such approach allows linearizing the problem of fluid dynamics.…”

Section: Solutions and Discussionmentioning

confidence: 99%

Mathematical model of elastic ribbed shell dynamics interaction with viscous liquid pulsating layer

Kondratov¹,

Kondratova²,

Mogilevich³

et al. 2015

ams

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The mechanical model of the system representing a ribbed pipe of ring like profile, formed by two surfaces of the coaxial cylindrical shells interacting with viscous incompressible liquid, the outer of which is geometrically irregular, and inner one is an absolutely rigid cylinder under the effect of the harmonic pressure 3526 D. V. Kondratov et al. pulsation at pipe ends is considered. The mathematical model of this system, consisting of differential equations in partial derivatives presenting dynamics of viscous incompressible liquid and an elastic ribbed shell together with boundary conditions is constructed. Expressions for amplitude frequency characteristics of outer geometrically irregular shell are discovered.

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Section: Solutions and Discussionmentioning

confidence: 99%

Mathematical model of elastic ribbed shell dynamics interaction with viscous liquid pulsating layer

Kondratov¹,

Kondratova²,

Mogilevich³

et al. 2015

ams

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“…Papers [6][7][8] are devoted to the harmonically vibrating indefinitely long beam-strip damping on the layer of compressible and incompressible liquid. Paper [9] deals with consideration of vibrating discs interaction with viscous incompressible liquid layer between them. The analogous problem for two vibrating plate is considered in [10].…”

Section: Introductionmentioning

confidence: 99%

Mathematical model of three-layer plate interaction with viscous incompressible liquid layer under foundation vibration

Грушенкова¹,

Mogilevich²,

Popov³

et al. 2015

ams

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The mathematical model for three-layer plate sagging oscillations, forming the wall of slit channel is worked out. The mathematical model presents non-linear connected system, consisting of: Navier-Stocks equations and continuity equation for liquid; the dynamics equations of three-layer plate with incompressible filler. The boundary conditions are presented by: the conditions of liquid adhesion to channel walls; the condition of free leakage of liquid at channel butt ends; the conditions of simply supported edge for three-layer plate. The mathematical linearization is made by means of perturbation method. The resulting problem was solved by means of the plate displacements assigned forms method for the stationary harmonic oscillations.

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“…The damping qualities of the liquid, conditioned by its viscosity are not considered in the references mentioned above. The problem of vibrating discs interaction with viscous incompressible liquid layer between them is solved in [11]. The present paper studies the case, where the discs are considered to be rigid and the case with one of the discs being elastic.…”

Section: Introductionmentioning

confidence: 99%

Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation

Kondratov

Mogilevich

Popov

et al. 2018

J. Phys.: Conf. Ser.

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Abstract. The forced hydroelastic oscillations of a circular plate resting on elastic foundation are investigated. The oscillations are caused by a stamp vibration under interaction with a plate through a thin layer of viscous incompressible liquid. The axis-symmetric problem for the regime of the steady-state harmonic oscillations is considered. On the basis of hydroelasticity problem solution the laws of plate deflection and pressure in the liquid are found. The functions of the amplitudes deflection distribution and liquid pressure along the plate are constructed. The presented mathematical model provides for investigating viscous liquid layer interaction dynamics with a circular plate resting on an elastic foundation. The above-mentioned model makes it possible to define the plate oscillations resonance frequencies and the corresponding amplitudes of deflection and liquid pressure, as well. Keywords -circular plate; hydroelastic oscillations; vibration stamp; viscous liquid; Winkler foundation IntroductionThe investigations of the plates and supporting elastic foundations interaction are of theoretical, as well as of practical interest. For example, the review [1], devoted to this subject matter, considers the items of elastic foundations development models, as well as various approaches to analytical and numerical investigation of beams and plates with elastic foundations interaction. Reference [2] studies free and forced oscillations of a circular plate, the plate resting on Winkler foundation. The investigation is carried out in axis-symmetric setting for the cases of a simply supported edge and a clamped one. Reference [3] studies stability and oscillations of circular polar orthotropic plates of variable thickness resting on Winkler foundation. The cases of the simply supported and clamped edge of the plates are considered. Reference [4] deals with investigation of oscillations of a thin circular plate with elastic fixation along the contour, the plate resting on Winkler elastic foundation. Reference [5] studies free oscillations of thin circular plate on Winkler foundation. The axis-symmetric problem under the condition of foundation rigidity change in radial direction is investigated in the above-mentioned reference. References [6,7] consider oscillations and stability of multi-layered circular plates on elastic foundation under the impact of local and distributed loadings of various nature. The Winkler and Pasternak models are used for foundation reactions modelling. On the other hand, the investigations of hydroelastic interaction of circular plates with an ideal liquid are of

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Investigation of the interaction between a viscous incompressible fluid layer and walls of a channel formed by coaxial vibrating discs

Cited by 25 publications

References 2 publications

Mathematical model of elastic ribbed shell dynamics interaction with viscous liquid pulsating layer

Mathematical model of elastic ribbed shell dynamics interaction with viscous liquid pulsating layer

Mathematical model of three-layer plate interaction with viscous incompressible liquid layer under foundation vibration

Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation

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