Vibration isolation performance and optimization design of a tuned inerter negative stiffness damper

• The transmissibility and stability conditions of a TINSD vibration isolation system are derived, and the closed-form solutions for H ∞ and H 2 optimization are obtained. • The parameter analyses are performed, and the most sensitive parameter is obtained. • A parameter optimization method for isolators is proposed, which is superior to H ∞ and H 2 optimizations under seismic excitations. • The seismic response control effect of a TINSD based on a realistic structure is studied, which is superior to that of a TID and TVMD. A tuned inerter negative stiffness damper (TINSD) is a vibration isolation and energy dissipation device providing a negative stiffness effect, which has the dual damping enhancement effect of negative stiffness and inertance. To date, there have been several studies on TINSDs; however, these studies are incomplete in terms of optimization, isolation system parameter analysis and application in seismic engineering. Therefore, a systematic study of a TINSD in an isolation system is needed. This paper presents a theoretical and numerical study of a SDOF-TINSD system and a realistic structure-TINSD subjected to ground motion. The absolute transmissibility and stability condition of the SDOF-TINSD are derived, and the absolute stiffness value of the negative stiffness element should be less than the primary structural stiffness. The TINSD parameters are optimized based on the H ∞ and H 2 norms, and analytical solutions for the optimal parameters are obtained. The parameter and sensitivity analyses of the TINSD are carried out. For a known inertance-mass ratio, the vibration isolation performance can be improved by the negative stiffness. The TINSD is very sensitive to deviations of the positive stiffness ratio, and its optimal parameters require special attention. Finally, the vibration control effect of the optimal TINSD is evaluated for harmonic excitation, stationary random excitation and seismic excitation, and an optimization method based on nonstationary random seismic waves (NRSW) for isolators in realistic structures is proposed. The control effect of the TINSD is better than that of the TID and TVMD with the same inertance-mass ratio. Moreover, the TINSD optimized by NRSW has a better seismic response control effect than the H ∞ and H 2 optimization methods.