Mathematical Modeling of Hydroelastic Oscillations of the Stamp and the Plate, Resting on Pasternak Foundation

Mogilevich, L. I.; Popov, V. S.; Popova, A. A.; Christoforova, A. V.

doi:10.1088/1742-6596/944/1/012081

Cited by 6 publications

(6 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The zig-zag hypothesis is valid for the three-layer beam, i.e. Kirchhoff hypothesis is valid for bearing layers, as well as the normal in the beam filler remains straight and turning by the angle [13][14][15][16][17]. Let us connect Cartesian coordinate with the center of beam filler medium surface in an undisturbed state.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Bearing in mind Eqs. (13), (21) According to Eqs. (19), (20) and (17), we find the expressions for and :…”

Section: The Theorymentioning

confidence: 99%

“…The problem of the bending hydroelastic oscillations of the plate under the impact of the viscous liquid pulsating layer was studied in [11]. The study of the hydroelastic oscillations of the plate, resting on Winkler foundation was made in [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical modeling of three-layer beam hydroelastic oscillations

Mogilevich¹,

Popov²,

Popova³

et al. 2017

Vib. proced.

View full text Add to dashboard Cite

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.

show abstract

Section: Statement Of the Problemmentioning

confidence: 99%

“…Bearing in mind Eqs. (13), (21) According to Eqs. (19), (20) and (17), we find the expressions for and :…”

Section: The Theorymentioning

confidence: 99%

See 1 more Smart Citation

Mathematical modeling of three-layer beam hydroelastic oscillations

Mogilevich¹,

Popov²,

Popova³

et al. 2017

Vib. proced.

View full text Add to dashboard Cite

show abstract

“…The equation of the bending oscillations of the plate, resting on Pasternak foundation, can be written down, as in references [21,25]:…”

Section: The Theorymentioning

confidence: 99%

“…The hydroelastic oscillations of the rectangular plates, resting on Pasternak foundation and interacting with an ideal incompressible liquid with a free surface, are investigated in references [17][18][19]. The investigation of the oscillations of the plate, resting on the elastic Winkler foundation and interacting with viscous incompressible liquid pulsating layer, was made in references [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Hydroelastic oscillation of a plate resting on Pasternak foundation

Kondratov¹,

Mogilevich²,

Popov³

et al. 2017

Vib. proced.

View full text Add to dashboard Cite

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.

show abstract