A framework for nonlinear peak response evaluation from linear response spectra of base-isolated structures using the bilinear hysteretic model

Abstract

This paper proposes a simple computational framework that can account for both properties of the base-isolated structure using the bilinear hysteretic model and reliably evaluate the nonlinear peak response without nonlinear response history analysis. The proposed computational framework requires the construction of new non-proportional damping models that match the base-isolated structure to accurately decompose the nonlinear multi-degree-of-freedom structure into multiple single-degree oscillators with intrinsic frequencies and damping ratios by equivalent linearization and complex-mode superposition methods. Each oscillator is excited by a response spectrum matching its own damping ratio, and this procedure is iteratively computed until the displacement error of the isolation layer achieves a preset value. Simultaneously, the peak nonlinear response of interest is calculated using the complex-mode-superposition complete square combination rule. The effect of peak response on nonlinear parameters is analyzed using a typical numerical example, and the relative error values for the applicable range are presented. Parametric research demonstrates that the new non-proportional damping matrix accurately reflects the modal characteristics of the base-isolated structure and prevents Rayleigh damping from suppressing the first-order modal characteristics. The particular example evaluation shows that the computational framework can effectively evaluate the nonlinear peak response of the BIS, with the isolation layer displacement error controlled within +5 %, the bottom shear force error within +20 %, and the top acceleration error between −10 % and +25 %.