Abstract
This paper considers the mathematical model statement for studying the hydroelastic oscillations of a narrow channel bottom resting on an elastic foundation with cubic nonlinearity. The parallel-walled channel filled with pulsating viscous incompressible fluid was investigated. The upper channel wall was assumed to be solid, and the channel bottom was represented as an elastic plate. The plane coupled hydroelasticity problem for the channel under consideration was formulated for the case of a given law of pressure changes at the channel ends. The fluid motion was assumed to be cree** one due to the channel narrowness and was studied within the framework of the hydrodynamic lubrication theory. The perturbation method was used to study the hydroelasticity problem under consideration. As a result, the nonlinear equation for the hydroelastic oscillations of the plate resting on the nonlinear elastic foundation was obtained. Initially, this equation was solved by the Bubnov-Galerkin method. Then, the harmonic balance method was used to determine the primary hydroelastic response of the channel bottom as the elastic plate resting on the elastic foundation with hardening cubic nonlinearity.
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The study was funded by Russian Science Foundation (RSF) according to the project No. 23–29-00159.
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Kondratov, D.V., Kondratova, T.S., Popov, V.S., Popova, M.V. (2023). Modeling Hydroelastic Response of the Channel Wall Resting on a Nonlinear Elastic Foundation. In: Radionov, A.A., Gasiyarov, V.R. (eds) Proceedings of the 9th International Conference on Industrial Engineering. ICIE 2023. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-38126-3_27
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