Stochastically Excited Nonlinear Systems

• Autorzy: Wagner U.
• Konferencja: Polish-German Workshop on Dynamical Problems of Mechanical Systems (10 ; 3-7.09.2007 ; Goslar, Germany)
• Języki publikacji: EN

Abstrakty

EN

The solution of high dimensional probability density functions of nonlinear mechanical systems by solving the corresponding Fokker-Planck equation constitutes still a serious problem. The paper gives an overview of a method proposed by the author which was applied successfully for a wide range of nonlinear systems. This method is illustrated by an example from vehicle dynamics. Additionally nonlinear systems are considered which contain multiple stable stationary solutions in the deterministic case. These systems are excited by an additional white noise resulting in interesting shapes of probability density functions which are calculated by solving Fokker-Planck equations. Ali results are compared by corresponding Monte Carlo simulations.

Słowa kluczowe

EN

stochastic systems; mechanical system; Fokkier-Planck equation

PL

system stochastyczny; system mechaniczny; równanie Fokkera-Plancka

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Problems
• Rocznik: 2007
• Tom: Vol. 31, No. 2
• Strony: 140--154
• Opis fizyczny: Bibliogr. 15 poz., rys., wykr.

Twórcy

autor

Wagner U.

• Technische Universität Berlin, Department of Applied Mechanics,

Bibliografia

• Bergman, L.A., 1992, On the Numerical Solution of the Fokker-Planck Equation for Nonlinear Stochastic Systems, Nonlinear Dynamics, 4, 357-372.
• Bergman, L.A., 2005, Application of multi-scale finite element methods to the solution of the Fokker-Planck equation, Computer methods in applied mechanics and engineering, 194, 1513-1526.
• Hsu, C.S., 1980, A Theory of Cell-to-Cell Mapping Dynamical Systems, Journal of Applied Mechanics, 47, 930-939.
• Hsu, C.S., 1991, Effects of Small Random Uncertainties on Non-Linear Systems Studied by the Generalized Cell Mapping Method, Journal of Sound and Vibration, 147 (2), 185-201.
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• Naess, A., 2000, Efficient path integration methods for nonlinear dynamic systems, Probabilistic Engineering Mechanics, 15, 221-231.
• Naess, A., 2006, Response probability density functions of strongly non-linear systems by the path integration method, International Journal of Non-Linear Mechanics, 41, 693-705.
• Knothe, K., Böhm, F., 1999, History of Stability of Railways and Road Vehicles, Vehicle System Dynamics, 31, 283-323.
• Sobczyk, K., 1998, Stochastic Nonlinear Systems, Existing Methods and New Results, ZAMM78 (10), 651-661.
• Sperling, L., 1988, Biorthogonale Entwicklungen von Verteilungsdichten und ihre Anwendungen ihre Analyse stochastischer Systeme, Teil I: Mathematische Grundlagen, ZAMM68 (7), 289-298.
• Sperling, L., 1990, Biorthogonale Entwicklungen von Verteilungsdichten und ihre Anwendungen żur Analyse stochastischer Systeme, Teil II: Beispiele, ZAMM 70 (10), 421-438.
• von Wagner, U., Wedig, W.V., 1999, Extended Laguerre-Polynomials for Nonlinear Stochastic Systems, Computational Stochastic Mechanics, ed. P.D. Spanos, A.A. Balkema, Rotterdam, Brookfield, 293-298.
• von Wagner, I.L, Wedig, W.V., 2000, On the Calculation of Stationary Solutions of Multi-Dimensional Fokker-Planck Equations by Orthogonal Functions, Nonlinear Dynamics 21(3), 289-306.
• von Wagner, U., 2002, On Double Crater-Like Probability Density Functions of a Duffing Oscillator Subjected to Harmonic and Stochastic Excitation, Nonlinear Dynamics, 28, 343-355.
• von Wagner, U., 2004, On Nonlinear Stochastic Dynamics of Quarter Car Models, International Journal of Non-Linear Mechanics, 39(5), 753-765.