Analysis of bilinear hysteretic structures with nonlinear fluid viscous dampers using modified stochastic linearization technique

Abstract

Viscous dampers are increasingly used to design seismic resistant structures in modern construction due to their ability to reduce structural and non-structural damage by absorbing a large portion of the earthquake input energy. To facilitate the design of such complex nonlinear systems, this study aims to propose new non-Gaussian probability density functions (PDFs) to improve the accuracy in the determination of the seismic response of bilinear hysteretic structures equipped with linearized nonlinear viscous dampers. The employed linearization method is based on a stochastic linearization technique using stationary response velocity PDFs, while the difference between the governing nonlinear differential equation and the equivalent linear equation is minimized. To generate suitable functions, a Genetic Algorithm (GA) optimization method is adopted for both hard and soft soil-based structures equipped with nonlinear viscous dampers using three different power coefficients. The computational error of the employed modified stochastic linearization technique is then evaluated for single-degree-of-freedom (SDOF) systems under a set of five thousand randomly generated earthquake excitations with peak ground accelerations (PGAs) of 0.2 g to 0.6 g. The results indicate that the proposed method can significantly reduce (up to 80%) the computational errors. Subsequently, the lateral roof displacements of 5-story structures equipped with nonlinear viscous dampers are obtained under a set of natural ground motions using different linearization methods. It is shown that the proposed functions lead to the least error for both hard and soft soil-based structures compared to the accurate results.