Inerter location effect on the generalized tuned mass damper inerter control

This paper investigates the inerter location effect on the generalized tuned mass damper inerter (TMDI) control, in which the end of the inerter is located at any position of the primary structure. A good understanding of the inerter location effect can help us achieve an optimal generalized TMDI control. Two mass ratios weighting the mass amplification effect and negative stiffness effect are defined to understand the inerter location effect. Based on the two mass ratios, the relationship between the TMD and generalized TMDI is established, the analytical solution of the optimal tuning frequency is derived, and a high-accuracy prediction equation judging whether the generalized TMDI performs better than the TMD is proposed. Finally, numerical analyses on a 76-story high building equipped with TMD and generalized TMDI are performed. The results show that the the generalized TMDI in fact is a large mass ratio TMD with a frequency-dependent stiffness, the generalized TMDI with larger inertance and smaller physical mass has more inerter location choices, and the damping ratio of the primary structure has no influence on the critical inerter location. The generalized TMDI considering the inerter location effect has better control effect than the TMD in suppressing both the wind-induced vibration and earthquake-induced vibration. The mean reduction ratios of peak floor accelerations for the TMD and TMDI controls are 60.53% and 54.5% under the wind-induced force excitation, and those of maximum floor drift ratios for the TMD and TMDI controls are 94.32%, 87.56% under the earthquake excitation.