On non-linear stochastic dynamics of quarter car models
In this paper, high-dimensional probability density functions of non-linear dynamical systems are calculated solving the corresponding Fokker-Planck equations. Zeroth approximations are derived from solutions of corresponding linear systems and analytical results for first- and second-order expected...
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Veröffentlicht in: | International journal of non-linear mechanics 2004-07, Vol.39 (5), p.753-765 |
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Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | In this paper, high-dimensional probability density functions of non-linear dynamical systems are calculated solving the corresponding Fokker-Planck equations. Zeroth approximations are derived from solutions of corresponding linear systems and analytical results for first- and second-order expected values. The zeroth approximations are used as weighting functions for the construction of generalized Hermite polynomials. The Fokker-Planck equation is expanded in terms of these polynomials and subsequently solved by a Galerkin method. As an example, models of a quarter car with non-linear damping subjected to white or colored noise excitation are considered. The damping is piecewise linear and asymmetric leading to a non-vanishing expected value of the displacement of the car. The excitation is realized by the roughness of the road and the car moves with constant velocity. Monte-Carlo simulations and analytical results are used for comparison. |
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ISSN: | 0020-7462 |
DOI: | 10.1016/50020-7462(03)00039-8 |