Seismic performance enhancement mechanism of MSDRC system with supplemental damping device

The multiple self-centering dual rocking core (MSDRC) system was proposed to mitigate the higher mode effects in the self-centering dual rocking core (SDRC) system, which was confirmed via the theoretical and nonlinear simulation analysis. However, the theoretical and simulation analysis results of the MSDRC system showed that abrupt displacement variations develop along the height of the MSDRC system under earthquakes, primarily occurring at the additional rocking sections. This paper aims to develop a simplified distributed parameter model to explore the seismic performance enhancement mechanism of the MSDRC system with supplemental damping device. The additional dampers are installed at rocking sections to suppress the abrupt displacement variations, especially under strong earthquakes. This paper focuses on the elastic dynamic response; the supplemental device is idealized as an equivalent rotational restraint rather than an explicit damping term. Parameter analysis was conducted to explore the influences of the design parameters on the performance of the MSDRC system with equivalent rotational restraint. The parameters include the comparative stiffness of the rocking core versus that of the gravity frame, and the comparative stiffness of the SFSDs versus that of the supplemental dampers installed at the rocking section. The dynamic evaluation covers the modal contribution factors, the displacement distribution, and the shear and moment distributions in the rocking cores and the steel frame. The analysis results indicate that the influence of the equivalent rotational restraint at rocking sections is not uniformly beneficial for all response quantities. While increasing R r can alleviate displacement discontinuity and reduce selected higher modal responses in the rocking cores, it may simultaneously amplify certain modal participation factors or higher modal contributions in other responses. The developed analytical model explicitly reveals these non-monotonic and parameter-dependent effects, which cannot be directly inferred from previous studies. Moreover, the derived characteristic equation and closed-form modal response solutions provide a direct tool for rapid preliminary evaluation of the effect of R r , without relying exclusively on complex nonlinear time-history analyses.