Third-order statistical linearization-based approach to derive equivalent linear properties of bilinear hysteretic systems for seismic response spectrum analysis

Abstract

Citation: Spanos, P. D. & Giaralis, A. (2013). Third-order statistical linearization-based approach to derive equivalent linear properties of bilinear hysteretic systems for seismic response spectrum analysis. Structural Safety, 44, pp. 59-69. doi: 10.1016Safety, 44, pp. 59-69. doi: 10. /j.strusafe.2012 This is the accepted version of the paper.This version of the publication may differ from the final published version. properties (ELPs), namely damping ratio and natural frequency, for bilinear hysteretic SDOF systems subject to seismic excitation specified by an elastic response/design spectrum. First, an efficient numerical scheme is used to derive a power spectrum satisfying a certain statistical compatibility criterion with the given response spectrum. Next, the thus derived power spectrum is used in conjunction with a frequency domain higher-order statistical linearization formulation to replace the bilinear hysteretic system by a third order linear system by minimizing an appropriate error function in the least square sense. Then, this thirdorder linear system is used to derive a second order linear oscillator possessing a set of ELPs by enforcing equality of certain response statistics of the two linear systems. The thus derived ELPs, are utilized to estimate the peak response of the considered nonlinear system in the context of linear response spectrum-based dynamic analysis. In this manner the need for numerical integration of the nonlinear equation of motion is circumvented. Numerical results pertaining to the European EC8 uniform hazard elastic response spectrum are presented to demonstrate the applicability and the usefulness of the proposed approach. These are further supported by Monte Carlo analyses involving an ensemble of 250 non-stationary artificial EC8 spectrum compatible accelerograms. It is believed that the proposed approach can be an effective tool in the preliminary aseismic design stages of yielding structures following either a force-based or a displacement-based methodology. Permanent

Accuracy of Equivalent Linear Models for Bilinear Oscillators Under Pulse-Like Ground Motion

“…The dynamic behavior of a bilinear SDOF oscillator subjected to seismic base accelaration is descrived by the following system of differential equations with zero initial conditions [4]:…”

“…Current approaches for deriving the equivalent linear properties are based on stochastic or deterministic analyses, see for instance Refs. [4][5][6][7] for an overview about some recent equivalent linear models of single-degree-of-freedom (SDOF) bilinear oscillators. Within this framework, it is worth highlighting that existing equivalent linear models for bilinear oscillators were developed without considering explicitly pulse-like near-fault ground motions, which seismological characteristics are different from the properties typically observed in case of far-field seismic events.…”

An Efficient Stochastic Linearisation Procedure for the Seismic Optimal Design of Passive Control Devices

“…Their algorithm consists in the definition of a non-parametric RS-consistent stationary PSD function and in the use of the SL in order to define the so-called equivalent linear parameters (ELPs) and, finally, in the estimation of the peak inelastic response of the non-linear oscillator. Since the applicability of this latter approach was limited to relatively mild non linear response, an higher-order SL scheme was further proposed in Spanos and Giaralis (2013) for the treatment of a wider class of hysteretic constitutive laws with a resulting higher accuracy. Recently, Mitseas et al (2018) proposed a novel stochastic dynamics framework to estimate the peak inelastic response of MDOF strongly non-linear system in a seismic context without undertaking non-linear step-by-step integrations of the response.…”

“…It is to remark that the more recent SL techniques for the determination of the seismic demand for hysteretic systems (Giaralis and Spanos, 2010;Spanos and Giaralis, 2013;Mitseas et al, 2018) can greatly benefit of these novelty aspects, both in terms of a significant reduction of the computational efforts in the derivation of RS-consistent PSD functions, and in accuracy, since some approximations in evaluating the response statistics can be removed without increasing the computational burden.…”

Elastic perfectly plastic oscillator under random loads: Linearization and response power spectral density

“…To the authors' knowledge, only one linearization procedure of either class has been proposed to linearize the EPP system. The first one is a (constant-parameter) Gaussian linearization [25,34,35]. The second one, which is based on a mean-square criterion, is the random-parameter linearization procedure described in [14].…”