STATIONARY AND NONSTATIONARY PROBABILITY DENSITY-FUNCTION FOR NONLINEAR OSCILLATORS

A method for the evaluation of the stationary and non-stationary proba bility density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the proba bility density function of the response in terms of C-type Gram-Charli er series expansion. By applying the weighted residual method, the Fok ker-Planck equation is reduced to a system of non-linear first order o rdinary differential equations, where the unknowns are the coefficient s of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived. (C) 19 97 Elsevier Science Ltd.