Original title: Galerkin-type solution of non-stationary aeroelastic stochastic problems
Authors: Fischer, Cyril ; Náprstek, Jiří
Document type: Papers
Conference/Event: Programs and Algorithms of Numerical Mathematics /22./, Hejnice (CZ), 20240623
Year: 2025
Language: eng
Abstract: The assessment of vibration characteristics in slender engineering structures, influenced by both deterministic harmonic and stochastic excitation, poses a challenging problem. Due to its complexity, transverse vibration of the structure (relative to the wind direction) is typically modelled using the single-degree-of-freedom van der Pol-type equation. Determining the response probability density function comprises solving the Fokker-Planck equation, a task that generally necessitates the use of approximate numerical methods. Some of these methods rely on Galerkin-type approximation employing orthogonal polynomial or exponential-polynomial basis functions. This contribution reviews available techniques for stationary and non-stationary cases and proposes some modifications while highlighting unresolved questions in the field.
Keywords: Fokker-Planck equation; Galerkin method; quasiperiodic response; random vibration; stochastic differential equation; van der Pol equation
Project no.: GA24-13061S (CEP)
Funding provider: GA ČR
Host item entry: Programs and Algorithms of Numerical Mathematics 22, ISBN 978-80-85823-74-5
Note: Související webová stránka: https://doi.org/10.21136/panm.2024.05

Institution: Institute of Theoretical and Applied Mechanics AS ČR (web)
Document availability information: Fulltext is available at the institute of the Academy of Sciences.
Original record: https://hdl.handle.net/11104/0366554

Permalink: http://www.nusl.cz/ntk/nusl-679026


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Research > Institutes ASCR > Institute of Theoretical and Applied Mechanics
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