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 performance 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.

惰性元件和负刚度 (NS) 元件都可以提高结构控制系统的控制效率。为了利用惰性和 NS 的双重优势，本研究开发了一种新的调谐惰性负刚度阻尼器 (TINSD)，用于结构的抗震保护。基于滚珠丝杠惯性和磁力感应 NS，展示了 TINS​​D 的实际实施方案。随后，采用定点法，考虑控制系统的稳定性，推导出单自由度结构抗震TINSD闭式设计方程。通过与具有相同惯性的 TID 和 TVMD 进行比较来评估 TINS​​D 的缓解性能，以及当主要结构受到谐波和静止随机地面运动时具有相同参数的惰性负刚度阻尼器（INSD）。此外，推导了与缓解率和能量耗散率相关的方程，以证明 TINS​​D 的性能增强原理。最后，当主要结构受到地震激励时，TINSD 的优越性能得到进一步验证。结果表明，在降低结构动力响应方面，TINSD 比 TID、TVMD 和 INSD 更有效。它可以利用惯性和NS的双重好处来提高阻尼器的能量耗散能力，从而可以通过增加惯性和负刚度来提高TINSD的性能。