Longitudinal and bending oscillations of a threelayered plate with compressible filler contacting with a viscous liquid layer
Deformable body mechanics
Аuthors
^{*}, ^{**}, ^{***}, ^{****}Yuri Gagarin State Technical University of Saratov, 77, Politechnicheskaya str., Saratov, 410054, Russia
*email: katenok.09041992@gmail.com
**email: mogilevichli@gmail.com
***email: vic_p@bk.ru
****email: anay_p@bk.ru
Abstract
The study of a threelayered 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 threelayered 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 endfaces. Oscillations of the threelayered plate are caused by the pressure pulsations at the channel endfaces. Pressure in the liquid layer changes herewith according to harmonic law.
The plane problem of longitudinal and bending hydroelastic oscillations of the threelayered plate was studied. The elastic displacements amplitudes of the threelayer 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 threelayered plate with compressible filler and liquid dynamics ones. The hydroelasticity problem was formulated. It consists of dynamic equations of the threelayered plate with compressible filler, as well as viscous liquid layer dynamic equations, namely NavierStokes 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 steadystate 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, threelayered plate, compressible filler, viscous liquid, pressure pulsationReferences

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