Dynamics of the Viscous Compressible Liquid Pulsating Layer Interaction with a Plate Resting on the Nonlinear Elastic Base

Abstract

The paper proposes a mathematical model of the viscous compressible liquid (gas) pulsating layer interaction with a plate mounted on the elastic base with rigid cubic nonlinearity. The plate is the lower wall of a narrow flat channel, which upper wall is assumed rigid. The case of an isothermal state is considered, where a given law of pressure alteration at the channel ends causes liquid pulsation. The model includes the Navier --- Stokes equations for viscous compressible liquid, continuity equation, equation of the barotropic medium state, equation of the Kirchhoff-type plate dynamics, boundary conditions at the dissimilar media and channel ends contact boundaries. The model asymptotic analysis is carried out using the perturbation method, and linearized equations are obtained for dynamics of the compressible viscous liquid thin layer. Using the iteration method, pressure distribution in the liquid layer is found. As a result, an integro-differential equation of flexural aeroelastic oscillations for a plate on the nonlinear elastic base is obtained. Based on the solution to this equation by the Bubnov --- Galerkin method, a generalized Duffing equation is obtained. It follows from the equation that liquid compressibility leads to a decrease in the inertial properties of the system under consideration and to the phase delay in the perturbing force. Using the harmonic balance method, the plate main aeroelastic response and its phase shift nonlinear characteristics are determined. Numerical study of these characteristics shows that accounting for the liquid compressibility leads to an increase in the plate resonant frequency and the oscillation amplitude values. The paper shows a possibility of suppressing the plate unstable oscillations with abrupt alteration in its deflection amplitudes by changing the liquid layer thickness

The study was funded by Russian Science Foundation (project no. 23-29-00159, https://rscf.ru/project/23-29-00159/)

Please cite this article in English as:

Popov V.S., Popova A.A. Dynamics of the viscous compressible liquid pulsating layer interaction with a plate resting on the nonlinear elastic base. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2024, no. 3 (114), pp. 45--69 (in Russ.). EDN: PHHPGG

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