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

Грушенкова, Е Д; Mogilevich, L. I.; Popov, V. S.; Rabinsky, Lev N.; Kuznetsova, Ekaterina

doi:10.12988/ams.2015.57482

Cited by 7 publications

(2 citation statements)

References 16 publications

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“…velocity movement projections on coordinates axis. The liquid dynamic equations are expanded by the boundary conditions: liquid adhesion to channel walls [16,17,20,21] 0…”

Section: Mathematical Formulationmentioning

confidence: 99%

Mathematical model of the plate on elastic foundation interacting with pulsating viscous liquid layer

Mogilevich¹,

Popov²,

Rabinsky³

et al. 2016

ams

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The problem of dynamic interaction of the plate on the elastic foundation with pulsating viscous incompressible liquid layer is set up and analytically solved. The problem in a flat setting for the regime of a stationary pulsating liquid movement in the cannel under the suggested difference of pressure at its butt end is considered. Deflections of plate are modeled as one-mass system elastic displacements. Parameters of one-mass system were found by using method of equivalent mass. The formulated boundary problem represents non-linear Navier-Stocks equations system for viscous incompressible liquid layer and the equation of one-mass system. The conditions of liquid adhesion to impenetrable channel walls and the condition of free leakage of liquid at channel butt ends are presented in the paper as the boundary ones. The linearization of the problem by means of perturbation method is made. The solution of the linearized problem is made by means of the assigned forms method for adjusted harmonic fluctuations.

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“…velocity movement projections on coordinates axis. The liquid dynamic equations are expanded by the boundary conditions: liquid adhesion to channel walls [16,17,20,21] 0…”

Section: Mathematical Formulationmentioning

confidence: 99%

Mathematical model of the plate on elastic foundation interacting with pulsating viscous liquid layer

Mogilevich¹,

Popov²,

Rabinsky³

et al. 2016

ams

Self Cite

View full text Add to dashboard Cite

show abstract

“…Reference [9] considers the bending oscillations of a flat channel wall, interacting with pulsating viscous liquid. References [10][11][12] investigate the hydroelastic oscillations of three-layered plates, interacting with viscous pulsating liquid, as well as under inertial excitation. References [13][14][15][16][17][18] research in the axis-symmetric problem of geometrically regular and ribbed cylinder shells, as well as the ones, forming an annular channel.…”

Section: Introductionmentioning

confidence: 99%

Bending oscillations of a cylinder, surrounded by an elastic medium and containing a viscous liquid and an oscillator

Mogilevich¹,

Popov²,

Kondratov³

et al. 2017

J. vibroeng.

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The article considers dynamic processes mathematical modeling in a mechanical system, consisting of an elastic hollow cylinder, surrounded by an elastic medium and containing viscous liquid and vibrating coaxial rigid cylinder. The amplitude frequency characteristic for investigating bending cylinder oscillations as one-mass system is defined. It is shown, that the constructed amplitude characteristic makes it possible to define the considered system resonance frequencies oscillations. The calculations demonstrated the significance of taking into account viscous liquid inertia and the surrounding elastic medium.

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Hydroelastic Vibrations of Circular Sandwich Plate Under Inertial Excitation

Kondratov

Mogilevich

Popov

et al. 2021

Advanced Structured Materials

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

Cited by 7 publications

References 16 publications

Mathematical model of the plate on elastic foundation interacting with pulsating viscous liquid layer

Mathematical model of the plate on elastic foundation interacting with pulsating viscous liquid layer

Bending oscillations of a cylinder, surrounded by an elastic medium and containing a viscous liquid and an oscillator

Hydroelastic Vibrations of Circular Sandwich Plate Under Inertial Excitation

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