Equivalent stochastic linearization for nonlinear uncertain structure under stationary Gaussian stochastic excitation

Equivalent stochastic linearization (ESL) for nonlinear uncertain structure under stationary stochastic excitation is presented. There are two parts of difference between the original system and equivalent system: one is caused by the difference between the means of original and equivalent stochastic structure; and another is caused by the difference between the original and equivalent stochastic structure which has the relation with stochastic variables. Statistical characteristics of equivalent stochastic structure can be obtained in accordance with mean square criterion, so nonlinear stochastic structure is transformed into linear stochastic structure. In order to attain that objective, the compound response spectrum of linear stochastic structure under stationary random excitation which is used in the solution is derived in the case of the mutual independence between stochastic excitation and stochastic structure. Finally, the example shows the accuracy and validity of the proposed method.