Longitudinal and bending oscillations of a three-layered plate with compressible filler contacting with a viscous liquid layer

Аuthors

Grushenkova E. D.^*, Mogilevich L. I.^**, Popov V. S.^***, Popova A. A.^****

Yuri Gagarin State Technical University of Saratov, 77, Politechnicheskaya str., Saratov, 410054, Russia

*e-mail: katenok.09041992@gmail.com
**e-mail: mogilevichli@gmail.com
***e-mail: vic_p@bk.ru
****e-mail: anay_p@bk.ru

Abstract

The study of a three-layered plate interaction with a layer of pulsating viscous incompressible liquid was performed. The liquid layer motion was regarded as a laminar one occurring in a narrow channel with parallel walls. Sticking conditions at the boundaries of liquid contact with the channel walls were assumed. The upper wall of the channel is being regarded absolutely rigid. The lower wall of the channel represents three-layered plate, and its bearing layers satisfy Kirchhoff's hypotheses. The plate filler is being regarded compressible in the transverse direction. The free support conditions are accepted at the plate end-faces. Oscillations of the three-layered plate are caused by the pressure pulsations at the channel end-faces. Pressure in the liquid layer changes herewith according to harmonic law.

The plane problem of longitudinal and bending hydroelastic oscillations of the three-layered plate was studied. The elastic displacements amplitudes of the three-layer plate were supposed to be much smaller than the thickness of the liquid layer in the channel. On the other hand, the longitudinal size of the channel was supposed to be much bigger compared to its transverse size. The hydroelastic problem consists of dynamics equations of the three-layered plate with compressible filler and liquid dynamics ones. The hydroelasticity problem was formulated. It consists of dynamic equations of the three-layered plate with compressible filler, as well as viscous liquid layer dynamic equations, namely Navier-Stokes and continuity equations. Accounting of normal and shear stresses, acting from the liquid side on the plate bearing layer contacting with it, is being performed while the experiment. Linearization of hydrodynamic equations was performed by the perturbation technique, and solution of the above said problem was obtained for the case of steady-state harmonic oscillations. Hydrodynamic parameters of the liquid layer were determined. Frequency dependent distribution functions of elastic displacements of the plate's layers and pressure of the viscous liquid layer were plotted.

Keywords:

hydroelasticity, oscillations, three-layered plate, compressible filler, viscous liquid, pressure pulsation

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