STATIONARY PROBABILITY DENSITY OF A CLASS OF NONLINEAR DYNAMICAL-SYSTEMS TO STOCHASTIC EXCITATION

The response of a dynamical system to Gaussian white-noise excitations may be represented by the Markov process whose probability density is governed by the well-known Fokker-Plank equation. In this paper a gen eral procedure is developed to obtain the solution for Fokker-Plank eq uation in the state of statistical stationary. The dynamical systems c onsidered are generally non-linear. This paper also demonstrates that the stationary joint probability density of the coordinates and veloci ty may possess the form of a separate product for the systems both non -linear damping and non-linear restoring forces.