A new modified stochastic linearization technique to analyze structures with nonlinear fluid viscous dampers

Abstract

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.

A novel stochastic linearization technique for structures with nonlinear fluid viscous dampers including soil-structure interaction

“…Case 2) If the probability density function (PDF) of the response velocity is assumed as a zero mean non-Gaussian PDF (Eq. (23) [17]), then the mathematical expectation of α+1 power of 𝑢̇ can be defined by Eq. (24).…”

“…Among the different alternatives proposed in the literature, stochastic linearization techniques (SLTs) have proven very efficient to linearize the force-velocity relationship of FVDs. SLTs are practical and convenient because they: a) linearize the nonlinear behavior of viscous dampers using a response spectrum analysis, and b) employ random earthquake simulations, contrary to the common assumption that earthquakes are harmonic [13][14][15][16][17][18]. Probabilistic SLTs also take into account the evolutionary characteristics of the earthquake input.…”

“…More recently, Asadpour et al [17][18] proposed a new modified SLT to analyze structures with nonlinear FVDs. The new SLT reduces the computational errors by using optimized non-Gaussian probability density functions (PDFs), which leads to more accurate results when applied to SDOF and MDOF systems.…”

“…The new SLT reduces the computational errors by using optimized non-Gaussian probability density functions (PDFs), which leads to more accurate results when applied to SDOF and MDOF systems. However, the method proposed by Asadpour et al [17][18] has to be extended to take into account potential SSI effects. Moreover, whilst past studies have focused on the linearization of FVDs, no study has examined SSI effects on the accuracy of the linearization exercise.…”