G. Muscolino et al., STATIONARY AND NONSTATIONARY PROBABILITY DENSITY-FUNCTION FOR NONLINEAR OSCILLATORS, International journal of non-linear mechanics, 32(6), 1997, pp. 1051-1064
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.