Seismic performance of base-isolated rigid-block systems enhanced by parallel tuned mass damper–inerter arrays

This study investigates the seismic performance of rigid-block-like structures equipped with a base isolation system enhanced by an array of parallel tuned mass damper–inerter devices (TMDIs). The protected structure, a typical data-center server rack, is modeled as a rigid cabinet that may experience uplift, rocking motion, and overturning under strong ground excitation. A comprehensive mechanical model is developed to describe the coupled rocking–translational dynamics of the cabinet, the isolation base, and the attached TMDI system, including impact and failure conditions. An extensive parametric investigation is carried out by varying the isolation period, the number and mass ratio of the TMDs, as well as the inertance associated with both the isolation base and the TMDs. The dynamic response is systematically evaluated through behavior maps, which identify full-contact, rocking, and overturning regimes in selected parameter planes. Numerical simulations are performed considering two cabinets with different slenderness and three historical earthquake records with distinct spectral characteristics. The results demonstrate that the proposed protection strategy is capable of significantly enlarging the safe response region, reducing both the minimum isolation period required to prevent uplift and the maximum displacement of the isolated base. Inerters attached to the TMDs are found to be particularly effective, while base-connected inerters provide additional benefits when combined with TMDIs. The effectiveness of the system is shown to depend on cabinet slenderness and seismic input characteristics. Overall, the study highlights the potential of parallel TMDI arrays as a robust and flexible solution for enhancing the seismic response of base-isolated rigid-block structures.