Inerter Location-Based Vibration Suppression Study of a Transmission Line Equipped with Tuned-Mass-Damper-Inerter (TMDI) under Harmonic Excitation

This paper proposes a novel ungrounded TMDI to improve the vibration suppression performance of the transmission line under harmonic excitation. This type of inerter-based damper may transform a translational motion into a rotational motion, greatly increasing the efficiency of vibration suppression. In the present study, the differential equations of motion are first derived based on the transmission line with an ungrounded TMDI structure. Then the closed-form solution of the displacement response spectrum considering the influence of the suspension location of the inerter is developed. The impact of the inerter location on vibration suppression performance is investigated in depth by defining the suspension location factor (upsilon) and tuning the damping ratio and frequency ratio. The results demonstrate that the suspension location of the inerter has a substantial impact on the damping ratio, frequency ratio, and vibration suppression performance. When the connection location of the inerter is near to the mass of the damper, it degrades the vibration suppression performance of the system. The failure phenomenon of the inerter occurs in the range of 0.2 < upsilon < 0.3, indicating that the presence of the inerter in this range does not enhance vibration suppression performance. The modal coordinate difference has a considerable impact on the vibration suppression efficacy of the TMDI. With increasing modal coordinate differences, the vibration suppression performance of the TMDI grows dramatically.