Modeling the dynamics of interaction of a compressed layer of a viscous compressible liquid with an elastic three-layer stator


Аuthors

Blinkova O. V.1*, Kondratov D. V.2**

1. Saratov State Academy of Law, 1, Volskaya str., Saratov, 410056, Russia
2. Yuri Gagarin State Technical University of Saratov, 77, Politechnicheskaya str., Saratov, 410054, Russia

*e-mail: oksana_parfilova@mail.ru
**e-mail: kondratovdv@yandex.ru

Abstract

With the constant development of mechanical engineering, space and aviation industries, the tasks of investigating the interaction of two elastic plates with a viscous liquid or gas between them are becoming more and more urgent. The study of elastic plates, the space between which is filled with a viscous liquid or gas, is becoming increasingly necessary. A mechanical system consisting of two plates interacting with each other through a layer of viscous compressible fluid in which constant pressure is maintained, as a result of which the upper absolutely rigid plate performs vertical oscillations is considered. The first plate is absolutely rigid - the vibrator, the second - is an elastic three-layer plate - the stator. The mathematical model in dimensionless variables is a coupled system of partial differential equations describing the dynamics of the motion of a viscous compressible fluid (Navier-Stokes equations and continuity equation) flowing between two plates with the corresponding boundary conditions. To solve the resulting problem of the interaction of a viscous compressible fluid and an elastic three-layer plate, we switched to dimensionless variables of the problem. Small parameters of the problem were chosen - the relative width of the viscous fluid layer and the relative deflection of the elastic stator. The selected small parameters of the problem made it possible to use the perturbation method to simplify the system of equations. The Bubnov-Galerkin method has found an expression for the amplitude-frequency characteristics of an elastic three-layer stator, further study of the expression will allow to identify and exclude resonant phenomena in structures of this type, take them into account when building new structures in modern mechanical engineering, aviation and space industries.

Keywords:

viscous compressible fluid, slit channel, a bar-strip, elastic three-layer plate, Navier-Stokes equation, amplitude-frequency characteristics (AFC)

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