Nonlinear Aeroelastic Oscillations in the Wall of a Flat Channel Filled with Viscous Gas and Resting on a Vibrating Foundation

This article considers the problem of aeroelastic oscillations in the channel wall having a suspension with hardening cubic nonlinearity, which were induced by the vibration of the channel foundation. The narrow flat channel formed by two parallel rigid walls and filled with pulsating viscous gas was...

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Main Authors: V. S. Popov, A. A. Popova
Format: Article
Language:English
Published: Kazan Federal University 2024-07-01
Series:Учёные записки Казанского университета: Серия Физико-математические науки
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Online Access:https://uzakufismat.elpub.ru/jour/article/view/71
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author V. S. Popov
A. A. Popova
author_facet V. S. Popov
A. A. Popova
author_sort V. S. Popov
collection DOAJ
description This article considers the problem of aeroelastic oscillations in the channel wall having a suspension with hardening cubic nonlinearity, which were induced by the vibration of the channel foundation. The narrow flat channel formed by two parallel rigid walls and filled with pulsating viscous gas was examined. The bottom wall was stationary, while the opposite one had a nonlinear elastic suspension. The aeroelasticity problem was formulated for the isothermal state of the gas and channel walls. Considering the narrowness of the channel, the equations of dynamics were derived for a thin layer of the viscous gas, and the asymptotic analysis of the problem was performed by the perturbation method. Using the method of iterations, the law of viscous gas pressure distribution in the channel was determined, and the equation of aeroelastic oscillations in the channel wall was obtained as a generalization of the Duffing equation. This equation was solved by the harmonic balance method. The primary nonlinear aeroelastic response of the channel wall and the nonlinear phase shift were expressed as implicit functions. These characteristics were studied numerically to evaluate the influence of the nonlinear elastic suspension of the channel wall and the viscous gas inertia and compressibility on the nonlinear oscillations in the channel wall.
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publishDate 2024-07-01
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record_format Article
series Учёные записки Казанского университета: Серия Физико-математические науки
spelling doaj-art-e6c6510393154c6c81a9c987787e5fe62025-02-03T12:00:35ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-07-01166222023710.26907/2541-7746.2024.2.220-23745Nonlinear Aeroelastic Oscillations in the Wall of a Flat Channel Filled with Viscous Gas and Resting on a Vibrating FoundationV. S. Popov0A. A. Popova1Yuri Gagarin State Technical University of Saratov; Institute of Precision Mechanics and Control, Russian Academy of SciencesYuri Gagarin State Technical University of SaratovThis article considers the problem of aeroelastic oscillations in the channel wall having a suspension with hardening cubic nonlinearity, which were induced by the vibration of the channel foundation. The narrow flat channel formed by two parallel rigid walls and filled with pulsating viscous gas was examined. The bottom wall was stationary, while the opposite one had a nonlinear elastic suspension. The aeroelasticity problem was formulated for the isothermal state of the gas and channel walls. Considering the narrowness of the channel, the equations of dynamics were derived for a thin layer of the viscous gas, and the asymptotic analysis of the problem was performed by the perturbation method. Using the method of iterations, the law of viscous gas pressure distribution in the channel was determined, and the equation of aeroelastic oscillations in the channel wall was obtained as a generalization of the Duffing equation. This equation was solved by the harmonic balance method. The primary nonlinear aeroelastic response of the channel wall and the nonlinear phase shift were expressed as implicit functions. These characteristics were studied numerically to evaluate the influence of the nonlinear elastic suspension of the channel wall and the viscous gas inertia and compressibility on the nonlinear oscillations in the channel wall.https://uzakufismat.elpub.ru/jour/article/view/71nonlinear aeroelastic oscillationelastically fixed wallviscous gasnonlinear elastic suspensionhardening cubic nonlinearityperturbation methodharmonic balance methodaeroelastic responsephase shift
spellingShingle V. S. Popov
A. A. Popova
Nonlinear Aeroelastic Oscillations in the Wall of a Flat Channel Filled with Viscous Gas and Resting on a Vibrating Foundation
Учёные записки Казанского университета: Серия Физико-математические науки
nonlinear aeroelastic oscillation
elastically fixed wall
viscous gas
nonlinear elastic suspension
hardening cubic nonlinearity
perturbation method
harmonic balance method
aeroelastic response
phase shift
title Nonlinear Aeroelastic Oscillations in the Wall of a Flat Channel Filled with Viscous Gas and Resting on a Vibrating Foundation
title_full Nonlinear Aeroelastic Oscillations in the Wall of a Flat Channel Filled with Viscous Gas and Resting on a Vibrating Foundation
title_fullStr Nonlinear Aeroelastic Oscillations in the Wall of a Flat Channel Filled with Viscous Gas and Resting on a Vibrating Foundation
title_full_unstemmed Nonlinear Aeroelastic Oscillations in the Wall of a Flat Channel Filled with Viscous Gas and Resting on a Vibrating Foundation
title_short Nonlinear Aeroelastic Oscillations in the Wall of a Flat Channel Filled with Viscous Gas and Resting on a Vibrating Foundation
title_sort nonlinear aeroelastic oscillations in the wall of a flat channel filled with viscous gas and resting on a vibrating foundation
topic nonlinear aeroelastic oscillation
elastically fixed wall
viscous gas
nonlinear elastic suspension
hardening cubic nonlinearity
perturbation method
harmonic balance method
aeroelastic response
phase shift
url https://uzakufismat.elpub.ru/jour/article/view/71
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