Optimal design of tuned inerter negative stiffness dampers with linear viscous and nonlinear eddy current damping for structural effective damping ratio enhancement

Tuned inerter negative stiffness damper (TINSD) has demonstrated its effectiveness in controlling structural vibrations. However, the potential to improve the effective damping ratio of primary structures remains unexplored, and thus far, TINSD has solely featured linear viscous damping. In this study, we explored two damping types for TINSD: linear viscous damping (abbreviated as TINSD) and nonlinear eddy current damping (termed EC-TINSD). The optimal design of the TINSD was conducted based on the effective damping ratio enhancement (EDRE) effect. Our findings reveal that an increase in the absolute value of the negative stiffness does not result in a continuous improvement in the control efficiency and effectiveness of TINSD, which correspond to the EDRE effect and the structural effective damping ratio, respectively. Importantly, we observe that the proposed optimal TINSD solution outperforms the one derived from the fixed-point method, particularly when the inertance ratio is less than 0.15. For EC-TINSD, its optimal design was performed based on the EDRE effect using statistical linearization techniques that employ both force-based and energy-based equivalent criteria. The control efficiency and effectiveness of optimal EC-TINSD were then validated through Monte Carlo simulation. This analysis highlights the significance of a large critical velocity for EC-TINSD to achieve greater accuracy in vibration control. Numerical studies were further conducted to investigate the control efficiency and effectiveness of ECTINSD under three types of real seismic excitations. The results demonstrate that both TINSD and EC-TINSD exhibit similar effectiveness in mitigating the maximum seismic responses of primary structures, and their efficiency surpasses that of viscous dampers and eddy current dampers with identical damping parameters. Additionally, the distinctive damping force limiting characteristic of EC-TINSD should be commended as it can protect the security and dependability of both the dampers and their connections to the structures.