Performance‑efficiency co-optimization for a novel eddy-current-based tuned negative stiffness inerter damper

This paper proposes a novel eddy‑current based tuned negative‑stiffness inerter damper (EC‑TNSID), which integrates nonlinear eddy-current damping into a tuned negative‑stiffness inerter damper. A performance-efficiency co-optimization framework is established for Gaussian and non‑Gaussian stochastic excitations, unifying force- and energy-based equivalence criteria. A reduced-order modal model of the EC-TNSID for multi-story structures is formulated. In this model, the critical velocity—a key parameter governing nonlinear damping—retains its original definition, enabling a consistent and simplified design. Four closed‑form optimal solutions are derived by combining two statistical scenarios (Gaussian/non-Gaussian) with two equivalence criteria (force/energy-based). Monte Carlo simulations validate the analytical predictions. While eddy-current damping features excellent durability, it suffers from strong nonlinearity and performance degradation at high velocities. This study demonstrates that appropriate setting of the critical velocity can secure the theoretically predicted performance and efficiency. Comparative evaluations under white-noise and real seismic records yield a statistically grounded rule: for Gaussian-optimized EC-TNSIDs, the force-based criterion is superior; for non-Gaussian-optimized designs, the energy-based criterion performs better. With the proposed performance-efficiency co-optimization, the EC-TNSID and its linear counterpart (TNSID) significantly outperform conventional devices (EC-TID, TID, ECD, VD) in mitigating seismic responses across both single-degree-of-freedom and multi-story structures. Among all configurations, the energy-based non-Gaussian design achieves the greatest response mitigation, along with the most favorable stroke and velocity demands on the damping element. The proposed EC-TNSID, together with its performance-efficiency co-optimization framework, provides a practical, high-performance and cost-effective control strategy to improve the seismic resilience of engineering structures. The findings are limited to linear structural systems, idealized device representations, and first-mode-targeted designs, while physical prototype validation remains to be conducted.