Accuracy and Limitations of the Method of Equivalent Linearization for Hysteretic Multi-Storey Structures
A method of solution for determing the response statistics of a nonlinear hysteretic shear building subjected to nonstationary stochastic excitation is suggested by utilizing a stochastic equivalent linearization technique. This paper concentrates on the accuracy of the predicted response for an excitation ranging from low to high intensity and on the computational efficiency of the time step procedure. The nonlinear hysteretic properties of the shear building are modelled by Bouc’s  model in terms of auxiliary variables following nonlinear differential equations. The auxiliary variables are linearized leading to a set of linear differential equations. They are solved numerically using the state vector formulation and a complex modal analysis time-step procedure in order to consider the time varying linearization coefficients. The procedure is applied to a six storey shear building with no residual linear stiffness to demonstrate the applicability to this special case. For the numerical efficiency of the time step procedure, a generalized Jacobi-iteration is suggested to solve in each time step efficiently the characteristic value problem. The predicted variances are then compared with the variances obtained by applying simulations procedures. The agreement is excellent for the velocity response, but less satisfactory for the displacement response. Finally, probability densities of response quantities are shown (based on 3000 simulated samples).
KeywordsAuxiliary Variable Hysteretic Behavior Equivalent Linearization Velocity Response Jacobi Method
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