Estimating the “effective period” of bilinear systems with linearization methods, wavelet and time-domain analyses: From inelastic displacements to modal identification

Abstract

This paper revisits and compares estimations of the effective period of bilinear systems as they result from various published equivalent linearization methods and signal processing techniques ranging from wavelet analysis to time domain identification. This work has been mainly motivated from modal identification studies which attempt to extract vibration periods and damping coefficients of structures that may undergo inelastic deformations. Accordingly, this study concentrates on the response of bilinear systems that exhibit low to moderate ductility values (bilinear isolation systems are excluded) and concludes that depending on the estimation method used, the values of the "effective period" are widely scattered and they lie anywhere between the period-values that correspond to the first and the second slope of the bilinear system. More specifically, the paper shows that the "effective period" estimated from the need to match the spectral displacement of the equivalent linear system with the peak deformation of the nonlinear system may depart appreciably from the time needed for the nonlinear system to complete one cycle of vibration. Given this wide scattering the paper shows that for this low to moderate ductility values (say 10   ) the concept of the "effective period" has limited technical value and shall be used with caution and only within the limitations of the specific application.

An analytical model of a deformable cantilever structure rocking on a rigid surface: experimental validation

“…fixed‐base linear elastic cantilevers) does not depend on the amplitude of the oscillations. Vibration of structures characterized by a bi‐linear force‐deformation response with hardening (a positive post‐yield stiffness) can be characterized by an effective period measure that depends, but not strongly, on the amplitude of the oscillations. However, the vibration period of rocking systems characterized by a rigid‐softening (negative post‐yield stiffness) behavior depends strongly on the amplitude of motion .…”

Evaluating the Accuracy of an Equivalent Linear Model in Predicting Peak Displacement of Seismic Isolation Systems using Single Friction Pendulum Bearings

“…The study proposed equations for predicting the accuracy of the predicted peak displacement as functions of isolation system's property and ground motion type. Beside these researches on isolation systems, there have been also many studies on the accuracy, limitation and improvement of the secant stiffness approach on other nonlinear systems [14][15][16][17][18][19][20].…”

A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra

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