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Two methods based on the Fourier method for studying the dynamics of an elastic wall of a square channel
| Title | Two methods based on the Fourier method for studying the dynamics of an elastic wall of a square channel |
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| Authors | A. S. Zharkova1, A. V. Ankilov1 1Ulyanovsk State Technical University |
| Annotation | The paper studies the dynamics of the wall of a three-dimensional square channel with an ideal incompressible fluid flow through it. The case of specifying a pressure change law at the inlet and outlet is considered. The channel is rigidly fixed on three sides and with an unfixed fourth elastic side (plate). Based on the constructed mathematical model described by a system of partial differential equations, the dynamics of an unfixed elastic channel wall is studied taking into account the interaction with the fluid flow in the incompressible medium model. The behavior of the elastic material of the plate is described by a linear model. The solution to the aerohydrodynamic part of the problem in the incompressible medium model is based on representing the desired gas pressure function as partial sums of double series, for finding the coefficients of which two methods are considered. In this case, the aerohydrodynamic load is determined through a function describing the unknown wall deflection, for which a partial differential equation is obtained, the solution of which is carried out using the Galerkin method. |
| Keywords | partial differential equations, dynamics, aerohydroelasticity, air duct, elastic plate, Fourier method, Galerkin method. |
| Citation | Zharkova A. S., Ankilov A. V. ''Two methods based on the Fourier method for studying the dynamics of an elastic wall of a square channel'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 95-100. Available at: https://conf.svmo.ru/files/2025/papers/paper19.pdf. - Date of access: 30.08.2025. |
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