Optimum design and performance evaluation of the tuned inerter-negative-stiffness damper for seismic protection of single-degree-of-freedom structures

Both the inerter and negative stiffness (NS) elements can improve the control efficacy of structural control systems. To utilize dual benefits of the inerter and NS, this study developed a new tuned inerter-negative-stiffness damper (TINSD) for seismic protection of structures. Based on the ball screw inerter and magnetic-force-induced NS, a practical implementation scheme of the TINSD is demonstrated. Subsequently, the closed-form design equation of the TINSD for seismic protection of a single-degree-of-freedom structure is derived by using the fixed-point method and considering the stability of the control system. The mitigation performance of the TINSD is evaluated by comparing with the TID and TVMD with the same inertance, as well as the inerter-negative stiffness damper (INSD) with the same parameters when the primary structure is subjected to harmonic and stationary random ground motions. In addition, the equation related to the mitigation ratio and the energy dissipation ratio is derived to demonstrate the performance enhancement principle of the TINSD. Finally, the superior perfor-mance of the TINSD is further verified when the primary structure is subjected to earthquake excitations. The results showed that the TINSD is more effective than the TID, TVMD, and INSD in reducing the dynamic response of structures. It can utilize the dual benefits of the inerter and NS to improve the damper energy dissipation capacity, and thus the performance of the TINSD can be improved by increasing the inertance and negative stiffness.