Interaction Dynamics Problem of a Layer, Being Squeezed, of Viscous Compressible Gas with Elastic Plate


DOI: 10.34759/trd-2020-110-21

Аuthors

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

1. Saratov State Academy of Law, 1, Volskaya str., Saratov, 410056, Russia
2. Volga Management Institute named after P.А. Stolypin, 164, Moskovskaya str., Saratov, 410012, Russia

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

Abstract

The rapid process of technology and engineering development in the modern world leads to the necessity of developing and considering mathematical models of thin-walled elastic structural elements. The study of elastic thin-walled structures, the space between which is filled with a viscous liquid or gas, is becoming increasingly interesting. The article tackles the problem of modeling the flow of a viscous compressible gas in a slotted channel consisted of two plates. The first plate is rigid, and performs harmonic vibrations in the vertical plane (vibrator), while the second one is represents an elastic plate (stator). Mathematical model in dimensionless variables is a coupled system of partial differential equations, describing motion dynamics of a viscous compressible gas (Navier-Stokes and continuity equations) flowing between two plates and an elastic beam-strip with the corresponding boundary conditions. To solve the set problem of a viscous incompressible gas and an elastic linear plate interaction, we switched to the dimensionless variables of the problem. Small parameters of the problem, i.e. relative width of the viscous gas layer and relative deflection of the elastic stator, were selected. These small parameters of the problem allowed using the perturbation method to simplify the system of equations. The article presents a technique for solving this problem, being a combination of the direct method for solving differential equations and the Bubnov-Galerkin method. An expression for the amplitude-frequency response of the elastic stator was obtained. The study of the amplitude-frequency response of the elastic stator will determine the operating modes under which the resonant phenomena occurs, and accounts for them when developing new structures in the modern engineering and aerospace industries. The presented mathematical model can find application in gas-dynamic vibration mounts and dampers.

Keywords:

viscous compressible gas, slit channel, a bar-strip, elastic single-layer plate, Navier-Stokes equation, amplitude frequency responce

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