Nonlinear viscous dampers can efficiently improve the seismic performance of structures by dissipating large amounts of earthquake-induced energy. In common practice, the spectral analysis of structures with nonlinear viscous dampers is generally conducted based on an estimated equivalent damping ratio. To this end, the stochastic linearization technique can be used as an effective probabilistic approach to take into account the evolutionary characteristics of the input earthquake excitation. This study aims to present optimal non-Gaussian probability density functions to improve the accuracy of the stochastic linearization technique for nonlinear viscous dampers in both firm and soft soil-based structures. It is shown that by using the optimum probability density functions, the computational error of the stochastic linearization technique for a single-degree-of-freedom structure under simulated ground motions, with a range of peak ground accelerations between 0.1 and 0.6 g, is reduced by up to 70%. The efficiency of the proposed probability density functions is then demonstrated for multi-degree-of-freedom structures, by estimating the roof displacements of a six-story steel frame with nonlinear viscous dampers under a set of natural ground motions using different linearization methods. The comparison of the stochastic linearization technique estimated responses with the exact values confirms that using the proposed probability density functions leads to considerably lower errors in both firm and soft soil-based structures compared with the other linearization techniques.
An investigation into accuracy, computation, and robustness of Stochastic Linearization of systems with saturation nonlinearities
