Novel distributed parameter models for self-centering dual rocking core system with multiple rocking sections

Higher mode effects can potentially magnify the internal forces and worsen the seismic performance of the self-centering dual rocking core (SDRC) system. Past research shows that the self-centering dual rocking core system with multiple rocking sections (MSDRC) can realize reduced internal force demands. However, the force demands of the SDRC system considering the high mode influences and the mitigation mechanisms of high mode contribution in the MSDRC system have not been systematically investigated. In this study, novel distributed parameter models were derived for the SDRC and MSDRC systems to study the internal force and explore the working mechanisms of multiple rocking sections in alleviating the high mode effects comparatively. The SDRC and MSDRC systems’ modal shape and the characteristic equations were analyzed to comparatively investigate how structural design parameters affect the dynamic characteristics and responses. The modal contributions were calculated to comparatively analyze the influences of the structural parameters on the superimposed responses. The analysis revealed that there was a clear contradiction between the reduction of higher modal contributions and the reduction of structural acceleration response in the SDRC system. The conflict could be resolved via the multiple rocking mechanism. The high modal vibration frequency was significantly reduced in the MSDRC system. The internal force demands and higher modal contributions were also decreased in the MSDRC system. The analysis results provided several suggestions for optimizing the stiffness design of the SDRC and MSDRC systems.