Galerkin-type solution of non-stationary aeroelastic stochastic problems

Fischer, Cyril, and Náprstek, Jiří. "Galerkin-type solution of non-stationary aeroelastic stochastic problems." Programs and Algorithms of Numerical Mathematics. 2025. 51-60. <http://eudml.org/doc/299969>.

@inProceedings{Fischer2025,
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.},
author = {Fischer, Cyril, Náprstek, Jiří},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {van der Pol equation; random vibration; stochastic differential equation; quasiperiodic response; Fokker-Planck equation; Galerkin method},
pages = {51-60},
title = {Galerkin-type solution of non-stationary aeroelastic stochastic problems},
url = {http://eudml.org/doc/299969},
year = {2025},
}

TY - CLSWK
AU - Fischer, Cyril
AU - Náprstek, Jiří
TI - Galerkin-type solution of non-stationary aeroelastic stochastic problems
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2025
SP - 51
EP - 60
AB - 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.
KW - van der Pol equation; random vibration; stochastic differential equation; quasiperiodic response; Fokker-Planck equation; Galerkin method
UR - http://eudml.org/doc/299969
ER -