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Stochastically Excited Nonlinear Systems

Wagner U.

Machine Dynamics Problems

2007

Vol. 31, No. 2

140-154

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.