| Title:
|
Galerkin-type solution of non-stationary aeroelastic stochastic problems (English) |
| Author:
|
Fischer, Cyril |
| Author:
|
Náprstek, Jiří |
| Language:
|
English |
| Journal:
|
Programs and Algorithms of Numerical Mathematics |
| Volume:
|
Proceedings of Seminar. Hejnice, June 23-28, 2024 |
| Issue:
|
2024 |
| Year:
|
|
| Pages:
|
51-60 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
van der Pol equation |
| Keyword:
|
random vibration |
| Keyword:
|
stochastic differential equation |
| Keyword:
|
quasiperiodic response |
| Keyword:
|
Fokker-Planck equation |
| Keyword:
|
Galerkin method |
| MSC:
|
35R60 |
| MSC:
|
37A50 |
| MSC:
|
65C30 |
| MSC:
|
65M60 |
| DOI:
|
10.21136/panm.2024.05 |
| . |
| Date available:
|
2025-06-02T07:39:47Z |
| Last updated:
|
2025-06-09 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703214 |
| . |
