Global–local mean square error criterion for equivalent linearization of nonlinear systems under random excitation

Abstract

The paper presents a dual approach with respect to the local mean square error criterion to multi-degree-of-freedom nonlinear systems under stationary Gaussian random excitation. It results in new values of linearization coefficients that are obtained as global averaged values of all local linearization coefficients. Two examples of typical two-degree-of-freedom nonlinear systems under zero-mean stationary Gaussian random excitation are demonstrated. The results show that the accuracy of solutions by the proposed criterion is significantly improved in comparison with the one by the classical equivalent linearization method, especially when the nonlinearity is strong.