Vibrations of the walls of a slot channel with a viscous fluid formed by three-layer and solid disks

Агеев, Р. В.; Mogilevich, L. I.; Popov, V. S.

doi:10.3103/s1052618814010026

Cited by 19 publications

(10 citation statements)

References 3 publications

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“…The problem of homogeneous plate sagging hydroelastic oscillations in the course of slit channel wall formation under viscous incompressible liquid layer pulsation at the assigned harmonic law of pressure at one butt end is set up and analytically solved in [14]. Papers [15][16][17] can be considered as the initiators of three-layer plate interaction with viscous liquid layer investigation. The above mentioned works consider the case of three-layer plate oscillations under harmonic law of an absolutely rigid channel wall movement or pulsating pressure in the liquid.…”

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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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 movement of thin viscous liquid layer can be considered as a creeping one [19]. Consequently, the dynamic equations of the liquid represent the Navier-Stokes equation without the inertia members, i.e.…”

Section: The Theorymentioning

confidence: 99%

“…But there is a shortage of studies devoted to the interaction of three-layer beams and plates with viscous liquid. For instance, the forced hydroelastic oscillations of the three-layered circular plate, interacting 1 3 with viscous incompressible liquid layer under the channel foundation vibration, are investigated in [19]. Alongside with this, the hydroelastic oscillations of three-layer beam are of theoretical and practical interest, too.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of three-layer beam hydroelastic oscillations

Mogilevich¹,

Popov²,

Popova³

et al. 2017

Vib. proced.

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Abstract. The problem of hydroelastic oscillations of three-layer beam interacting with viscous liquid layer is set up and analytically solved. The problem presents the equation system of a three-layer beam and Navier-Stokes equations. The following boundary conditions are chosen: the no-slip conditions, the conditions for pressure at the edges, the simply supported edges conditions. The problem is solved for the steady-state harmonic regime. The frequency dependent distribution functions of the beam deflection are constructed. The given function allows investigating the resonance hydroelastic oscillations of a three-layer beam, as well as its deflected mode.

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“…Reference [14] deals with solution of the problem of the bending hydroelastic oscillations of the plate, forming the narrow channel wall under the impact of the viscous liquid pulsating layer. The forced hydroelastic oscillations of the three-layered round plate interacting with viscous incompressible liquid layer under the channel foundation vibration are investigated in [15]. Alongside with this, the evaluation of foundation elasticity impact on hydroelastic oscillations is of theoretical and practical interest.…”

Section: Introductionmentioning

confidence: 99%

Hydroelastic oscillation of a plate resting on Pasternak foundation

Kondratov¹,

Mogilevich²,

Popov³

et al. 2017

Vib. proced.

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Abstract. The bending oscillations of the plate, resting in Pasternak foundation and interacting with a vibrating stamp through a thin layer of viscous incompressible liquid, are investigated. On the basis of hydroelasticity problem solution, the laws of the plate deflections and pressure in the liquid are found. The functions of the deflections amplitude distribution and liquid pressure along the channel are constructed. The obtained results allow to define oscillations resonance frequencies and to study viscous liquid interaction with elastic plates, resting on Pasternak foundation.

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Vibrations of the walls of a slot channel with a viscous fluid formed by three-layer and solid disks

Cited by 19 publications

References 3 publications

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

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

Mathematical modeling of three-layer beam hydroelastic oscillations

Hydroelastic oscillation of a plate resting on Pasternak foundation

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