Název: Galerkin-type solution of non-stationary aeroelastic stochastic problems
Autoři: Fischer, Cyril ; Náprstek, Jiří
Typ dokumentu: Příspěvky z konference
Konference/Akce: Programs and Algorithms of Numerical Mathematics /22./, Hejnice (CZ), 20240623
Rok: 2025
Jazyk: eng
Abstrakt: 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.
Klíčová slova: Fokker-Planck equation; Galerkin method; quasiperiodic response; random vibration; stochastic differential equation; van der Pol equation
Číslo projektu: GA24-13061S (CEP)
Poskytovatel projektu: GA ČR
Zdrojový dokument: Programs and Algorithms of Numerical Mathematics 22, ISBN 978-80-85823-74-5
Poznámka: Související webová stránka: https://doi.org/10.21136/panm.2024.05

Instituce: Ústav teoretické a aplikované mechaniky AV ČR (web)
Informace o dostupnosti dokumentu: Dokument je dostupný v příslušném ústavu Akademie věd ČR.
Původní záznam: https://hdl.handle.net/11104/0366554

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-679026