Dynamic Performance of Time-Domain Piecewise Linear Stiffness System

Abstract

This paper studies the dynamic performance of two kinds of time-domain piecewise linear stiffness systems, a piecewise positive-stiffness system (PPS) and a piecewise negative-stiffness system (PNS). The PPS is formulated by involving a positive-stiffness spring in the drifting stage of structural motion, whereas the PNS is formulated by introducing a negative-stiffness spring in the recentering stage of structural motion. To investigate the performance of the piecewise stiffness systems (PSSs), some fundamental analyses are conducted on the PPS and PNS compared with their respective continuous positive-stiffness system (CPS) and continuous negative-stiffness system (CNS), which have demonstrated the superior performance of the PPS over the continuous stiffness systems (CSSs). A PSS shows additional damping effect on the resonance responses and maintains part of the stiffness property compared with a CSS. Second, for the convenience of performance evaluation, the equivalent linearization of the PSS is studied to determine the equivalent stiffness and the equivalent damping of the equivalent linear system (ELS) of the PSS. The equivalent stiffness is derived after obtaining the equivalent period of the PSS, and the equivalent damping is obtained based on the equivalent energy in one cycle of steady-state harmonic vibration. Third, the accuracy of the ELS is analyzed by comparing the resonance frequency ratio and the resonance response ratio. Finally, the displacement reduction effect of the PSS is investigated under excitations from different soil conditions to consider the influence of the frequency of excitations.