Experimental study and dual-friction restoring force modeling of a symmetric negative stiffness device for rocking structures

This study proposes a symmetric negative stiffness rocking structure (SNRS) to enhance the seismic performance of rocking structures. The SNRS employs a symmetric layout to accommodate bidirectional rocking and achieve a controlled negative-to-positive stiffness transition. Quasi-static variable-amplitude reversed cyclic tests were conducted to evaluate its hysteretic and stiffness-switching behavior. A dual-friction restoring force model of the negative stiffness device (NSD) was developed from the load-transfer path and kinematic compatibility, incorporating disc-spring and journal friction. Experimental results show that the SNRS achieves the designed negative-to-positive stiffness transition, with a mean relative error below 10% between the measured and theoretical equivalent stiffnesses. The proposed dual-friction restoring force model captures the main hysteretic response, with R ² exceeding 0.90 at all tested loading amplitudes. Nonlinear time-history analyses further show that the SNRS reduces seismic demands across hazard levels, lowering base shear and floor acceleration by approximately 15% compared with a conventional energy-dissipating rocking system. Compared with the dual-friction model, the conventional elastic model overestimates the response by up to 17.6% in rocking rotation and 9.1% in inter-story drift. These findings support the design, evaluation, and modeling of negative stiffness mechanisms in rocking structures.