A hybrid approach for the time domain analysis of linear stochastic structures

•We proposed a hybrid method for linear stochastic dynamic structures.•A reduced stochastic model of the finite element model is developed.•The second order estimations of the mean and covariance matrices are obtained.•The results of the proposed method do not contain the secular terms.•The proposed method is quite suitable for the case of low levels of uncertainties. A new hybrid approach for the time domain analysis of linear stochastic structures with uncorrelated or correlated random variables is proposed. This new hybrid approach combines the modal approach, the second-order perturbation technique and the number theoretical method (NTM). In the hybrid approach, an approximate stochastic model of the finite element (FE) model is developed in the sense of first-order accuracy, which provides second-order estimations of the mean and covariance matrices of structural responses. Compared with the FE model, the proposed model is more convenient in terms of the computation effort it requires. By employing the NTM to evaluate the statistical moments of solutions of the approximate model, the secular terms, contained in the results of the perturbation stochastic finite element method, are eliminated. Two numerical examples are presented to demonstrate the accuracy and efficiency of the method proposed.