Fast Equivalent Linearization Method for Nonlinear Structures under Nonstationary Random Excitations

An efficient analysis procedure has been developed for the random vibration analysis of nonlinear structures subjected to nonstationary random excitations based on the equivalent linearization method and the time-domain explicit formulation method. When the equivalent linearization method is used for the nonstationary random vibration analysis of a nonlinear structural system, equivalent linear systems are constructed for different time instants and the analysis problem is transformed to a series of analyses of these linear systems. Because a large number of linear analyses must be conducted to get reliable results for the original nonlinear system, efficiency of the analysis algorithm for the linear analysis is crucial for its successful application. The time-domain explicit formulation method, recently proposed for the nonstationary random vibration analysis of linear systems, has much higher computational efficiency than other methods owing to the use of explicit expressions of dynamic responses of linear systems. Therefore, a numerical algorithm developed by combining these two methods will be highly efficient. The proposed method is applied to the random vibration analysis of Duffing systems and hysteretic systems under nonstationary excitations. Numerical examples indicate that the proposed approach is feasible and highly efficient.