Inerter Nonlinearity and Its Influence on Control Efficiency of TMDI for Suppressing Vortex-Induced Vibration of Bridges

Inerter-based dynamic vibration absorbers (IDVAs) have been theoretically studied in the vibration control of civil structures. However, experimental studies, especially studies on the nonlinearity of this mechanical device and its influence on the control efficiency of civil structures, are limited. In the present study, a ball-screw inerter aimed to control the vortex-induced vibration (VIV) of a scaled bridge model is designed and manufactured. The dynamic property of this device is examined through experiments. A nonlinear physical model is proposed to simulate this device and is incorporated into the governing equations of the bridge-TMDI (tuned mass damper inerter) system to investigate its influence on VIV control efficiency. Design suggestions on how to mitigate the influence of inerter nonlinearity are also proposed. The results indicate that the dynamic property of the ball-screw inerter depends on the magnitude of driving acceleration. With the increment of acceleration magnitude, the ball-screw inerter approaches an ideal linear inerter. Due to this acceleration-dependent property, the control efficiency of the TMDI when considering the inerter nonlinearity is worse than that of an ideal linear TMDI. By retuning the optimum design parameters of a TMDI obtained based on linear assumption, the influence of inerter nonlinearity can be compensated to some extent. In addition, for a certain designed inertance, one can choose a larger diameter of a ball screw and a larger value of lead to further reduce the influence of inerter nonlinearity. Even though this design option will reduce the mass amplification ratio of the inerter, the actual physical mass of the inerter is still ignorable as compared with the mass of the TMDI mass block.