Parameter optimization and vibration reduction performance of the inerter negative-stiffness tuned mass damper

This paper proposes an inerter negative-stiffness tuned mass damper (INTMD), which aims to enhance the vibration control performance of structures under harmonic, pedestrian-induced and wind-induced excitations. The motion equation of a single degree of freedom with INTMD is derived, and the expressions of the dynamic amplification factor and the closed-form solution of the stability condition for the SDOF-INTMD system are obtained. The closed-form optimal parameters for the INTMD under harmonic excitations are derived based on the H _∞ criterion. Parameter analyses are performed on the INTMD system. The results demonstrated that the vibration reduction effect is highly sensitive to the stiffness and inerter. Additionally, the inerter stiffness and negative stiffness complement each other functionally. Finally, the vibration control performance of the optimally configured INTMD is quantitatively evaluated under harmonic and wind-induced excitations. The results show that the INTMD achieves significantly better vibration control effectiveness than both the conventional TMD and the Maxwell TMD for the same mass ratio.