Control Algorithm for Distributed Multiple Semiactive Tuned Mass Dampers in Base‐Isolated Buildings Under Earthquake Excitations

This study presents a generalized mathematical formulation and performance evaluation of an energy-based predictive (EBP) control algorithm for mitigating the seismic response of base-isolated (BI) multistory buildings equipped with distributed multiple semiactive tuned mass dampers (DM-SATMDs). Although base isolation effectively limits superstructure accelerations, it often results in large isolator displacements, particularly under strong or near-fault ground motions. To address this limitation, the EBP algorithm—originally developed for a single semiactive TMD—is extended herein to an arbitrary number of semiactive units distributed across multiple floor levels. The coupled equations of motion for BI buildings with DM-SATMDs are derived, and a comprehensive parametric study is performed considering different isolation periods, TMD parameters, and number of stories under real earthquake records. Four configurations are examined: BI without TMDs, BI with a single SATMD (S-SATMD), BI with multiple SATMDs (M-SATMDs) placed on the same floor, and BI with DM-SATMDs. The proposed strategy is further evaluated through floor response spectra (FRS), comparisons with existing passive and semiactive control strategies, robustness analyses, and a nonlinear lead–rubber bearing model accounting for heating-induced lead-core strength degradation. The results show that the proposed control algorithm is generally more effective for taller BI structures across all evaluated parameters. Notably, the BI + DM-SATMDs configuration promotes an effective redistribution of seismic energy between the isolation system and the auxiliary dampers. Further, the proposed EBP-controlled DM-SATMDs largely outperform S-SATMD and conventional DM-PTMDs in mitigating FRS across all considered earthquake records, enhancing floor acceleration control and secondary systems performance. Overall, the proposed EBP-based DM-SATMDs framework offers an efficient and adaptable strategy for improving the seismic resilience of BI structures.