Probability density function of MDOF structural systems under non-normal delta-correlated inputs

A method to approximate the probability density function of MDOF linear systems under non-normal delta-correlated input is presented. The method requires: (i) the evaluation of the response cumulants up a given order, by solving the set of cumulant differential equations; (ii) the evaluation of the quasi-moments of the response by means of recursive relationships, once the response cumulants are known; (iii) the evaluation of the coefficients of the C-type Gram-Charlier series expansion of the response probability density function, by solving a set of linear algebraic equations, whose known terms depend on the quasi-moments of the response up to a given order. The numerical application shows the versatility and the accuracy of the proposed method.