A dual criterion of stochastic linearization method for multi-degree-of-freedom systems subjected to random excitation

In this paper, a dual criterion of stochastic linearization method is developed for multi-degree-of-freedom systems subjected to random excitation. A closed system is obtained for determining coefficient matrices of the linearized system. Two examples of two-degree-of-freedom systems subjected to random excitation are presented. The mean-square responses obtained by the dual approach are compared with those obtained by two other methods, namely, conventional linearization technique and energy method. The results show that the dual criterion gives a good prediction on mean-square responses of the original nonlinear system when the nonlinearity is increasing.