Enhanced Energy Dissipation of Tuned Negative Stiffness Viscous Mass Damper (TNSVMD) for the Base-Isolated Structure (BIS)

Negative stiffness dampers (NSDs) have garnered significant attention in the research of base-isolated structures (BIS). This study proposes a tuned negative stiffness viscous mass damper (TNSVMD), which includes a tuning spring in series with the NSD and an inerter, to enhance the seismic control effect of the BIS. An analytical model of a BIS with the TNSVMD is initially established, followed by an investigation into frequency response analysis. The analytical expressions for the stochastic responses of the BIS with TNSVMD are derived, and further exploration is conducted on the influences of the negative stiffness ratio, dashpot damping ratio, and inerter mass ratio on the stochastic responses of the BIS. The mechanisms responsible for the damping enhancement and energy dissipation enhancement of the BIS with the TNSVMD are elucidated through the derivation of the analytical solution for the effective damping ratio and dissipated energy of the BIS with the TNSVMD. Two principles are utilized to determine the optimal parameters of the TNSVMD. These principles involve minimizing the earthquake input energy ratio of the BIS and minimizing the stochastic displacement response of the BIS. Finally, the effectiveness of the TNSVMD is validated through a design example using 100 ground motions. The results indicate that the displacement and acceleration responses of the BIS can be simultaneously controlled due to the weakening of stiffness and enhancement of the effective damping ratio, leading to higher energy dissipation efficiency of the TNSVMD. The increase in the inertial mass ratio enhances the seismic mitigation effect and reduces the optimal negative stiffness ratio and optimal dashpot damping ratio. Therefore, it raises the possibility of implementing the TNSVMD. The inherent damping ratio of the BIS has a significant impact on the control efficiency of the TNSVMD. For BIS systems with relatively small inherent damping ratios, the TNSVMD can achieve better control effectiveness.