Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
van der Pol equation; random vibration; stochastic differential equation; quasiperiodic response; Fokker-Planck equation; Galerkin method
van der Pol equation; random vibration; stochastic differential equation; quasiperiodic response; Fokker-Planck equation; Galerkin method
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.
Search
Partner of
