Seismic Responses of Elastic Single‐Degree‐of‐Freedom Oscillators Fixed on Controlled Rocking Isolation Systems with Flag‐Shaped Hysteresis

Free rocking isolation systems (FRIS), characterized by negative post‐uplift stiffness, have demonstrated favorable seismic performance such as resonance avoidance and gravity‐driven self‐centering (SC); however, a key design challenge lies in simultaneously ensuring sufficient deformability of the rocking isolation story while effectively mitigating the seismic demand on the superstructure. To address this challenge, this study investigates controlled rocking isolation systems (CRIS) with flag‐shaped (FS) hysteretic devices. An analytical model is developed for elastic single‐degree‐of‐freedom (SDOF) oscillators (representing elastic low‐to‐medium rise frames) fixed on CRIS with FS hysteresis. A practical application using NiTi shape‐memory alloy (SMA)‐based rocking columns is proposed to realize the intended FS behavior. The analytical model is validated through comparisons with a newly developed finite element model in OpenSees. Dimensional analysis is employed to reduce the number of governing variables in the equations of motion, thereby facilitating the identification of fundamental similarities in seismic responses across different structural scales and loading conditions. Both case‐to‐case and statistical comparisons confirm the accuracy of the proposed model. Based on the validated model, parametric studies are performed to examine the effects of varying FS hysteretic parameters and seismic input characteristics on the structural seismic performance. The results further confirm that CRIS exhibit enhanced dynamic stability relative to FRIS. Furthermore, it is possible to achieve a balance between controlled rocking and minimized superstructure demand for CRIS with FS hysteresis.