Radial and Flexural Vibrations of the Round Three-Layered Plate Interacting with Pulsating Layer of a Viscous Liquid

DOI: 10.34759/trd-2020-110-6

Аuthors

Bykova T. V.^*, Mogilevich L. I.^**, Popov V. S.^***, Popova A. A.^****, Chernenko A. V.^*****

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

*e-mail: tbykova69@mail.ru
**e-mail: mogilevichli@gmail.com
***e-mail: vic_p@bk.ru
****e-mail: anay_p@bk.ru
*****e-mail: 3chav@mail.ru

Abstract

The presented work formulated and solved the problem of forced radial and flexural hydro-elastic vibrations of the round three-layer plate. The study of a plate with light incompressible filler under the action of normal and shear stresses from the side of the pulsating layer of the viscous incompressible liquid was performed. The axisymmetric problem, in which the plate was regarded as the lower wall of the narrow channel, filled with a viscous fluid, was studied. The fluid movement in the channel was considered as a creeping one. Equations of the three-layer plate dynamics were obtained based on the zigzag normal hypothesis and the D’Alembert principle. The developed mathematical model consists of dynamic equations of a viscous incompressible fluid layer and dynamic equations of the round three-layered plate. The following boundary conditions were selected:

– liquid sticking conditions to the channel walls;

– the liquid free-flow conditions at the channel end;

– the plate rigid fixing conditions;

– and conditions of limited liquid pressure and the deflection plate at the symmetry axis.

The hydrodynamic parameters distribution of the fluid layer as the plate deflection functions was found, and resolving equations for determining the plate elastic displacements were obtained. The amplitude-frequency responses of the radial and flexural plate displacements corresponding to the main mode for the steady-state harmonic oscillations were plotted. The numerical study of the radial and flexural oscillations amplitudes on the main mode, which demonstrated the mutual effect of the inertia and stiffness forces of the three-layered plate in the radial and normal directions, was performed. The performed computation revealed a significant impact of inertia forces in the normal direction on the amplitude-frequency response of the plate radial displacements. On the other hand, the computations showed a slight effect of inertial forces in the radial direction on the amplitude-frequency response of the plate deflections.

Keywords:

hydroelasticity, vibrations, viscous fluid, round three-layered plate

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