# Hydroelastic Response of Three-Layered Plate Interacting with Pulsating Viscous Liquid Layer

• V. S. Popov
• L. I. Mogilevich
• E. D. Grushenkova
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

## Abstract

The problem of longitudinal and bending oscillations of the sandwich plate interacting with the pulsating viscous fluid layer was investigated. The three-layered plate with an incompressible filler was considered. The model of viscous incompressible fluid was chosen to study viscous fluid dynamics. A mathematical model of the investigated mechanical system consists of dynamic equations of the three-layered plate with an incompressible filler, the Navier–Stokes equations and the continuity equation for a viscous incompressible fluid. The no-slip conditions and pressure coincidence at the edges with pressure in the surrounding liquid were selected as boundary ones. The plane problem of hydroelasticity was considered. We investigated the regime of steady harmonic oscillations. The dimensionless variables and small parameters were proposed to solve the problem. The solution of the hydroelastic problem was carried out by the perturbations method using the proposed small parameters of the problem. As a result, we obtained the linearization problem of hydroelasticity. The elastic displacement of the plate and the hydrodynamic parameters of the fluid were founded.

## Keywords

Hydroelasticity Oscillations Sandwich plate Viscous fluid Pulsating pressure Mathematical modeling

## Notes

### Acknowledgements

The study was funded by Russian Foundation for Basic Research (RFBR) according to the projects № 18-01-00127-a and № 16-01-00175-a.

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© Springer Nature Switzerland AG 2019

## Authors and Affiliations

• V. S. Popov
• 1
Email author
• L. I. Mogilevich
• 1
• E. D. Grushenkova
• 1
1. 1.Yuri Gagarin State Technical University of SaratovSaratovRussia