Exploring the performance of a nonlinear bi-modal tuned mass damper under seismic excitation

Nonlinear tuned mass dampers (NTMDs) and nonlinear energy sinks (NESs) are recognized as effective alternatives to classical linear tuned mass dampers (LTMDs), as they enable energy dissipation over a wider frequency band. This study investigates the performance of a nonlinear bi-modal tuned mass damper (NBMTMD), which can be classified as either an NES or an NTMD, for mitigating bi-directional seismic vibrations in buildings. The governing equations of motion for the building equipped with the proposed device are derived in two directions. To demonstrate its effectiveness, the NBMTMD is designed and optimized using both friction and viscous dampers, and new nonlinear formulations are developed to incorporate friction damping. The optimized device is then evaluated under several earthquake records. To highlight the wide frequency band covered by the NBMTMD, the building is analyzed under two conditions: with and without stiffness degradation. The results confirm that the NBMTMD effectively controls building vibrations during seismic excitations. Moreover, the proposed NBMTMD exhibits significantly better performance than the LTMD when the stiffness of the main structure is substantially reduced.