The role of auxiliary mass element in the dynamic performance of tuned-inerter devices

In the analysis of systems incorporating inerters, their physical mass is often neglected. In this study, the physical mass of the inerter device, as well as any intentionally introduced mass elements within the inerter system, are referred to as the auxiliary mass, and their influence on the performance of passive tuned inerter devices is examined. The inerter has attracted considerable attention in the earthquake engineering community due to its excellent feature as a mass amplifier device. A tuned inerter device is typically realized by combining an inerter with a spring and a dashpot. Alternatively, an inerter can be integrated into classical tuned mass damper systems, resulting in tuned inerter devices that incorporate auxiliary mass elements. Despite its significance, the role of the auxiliary mass element in tuned inerter devices has received limited attention in the literature. This study aims to fill this gap by examining how the auxiliary mass element impacts the overall effectiveness of these devices. Results reveal that the dynamic performance of tuned inerter devices with an auxiliary mass is strongly influenced by the connection point of the inerter element, whether to the lower or upper storey. In this paper, this phenomenon is investigated systematically in both SDOF and MDOF structures. Shake table experiments using harmonic motion input validate these findings, highlighting the critical role of the auxiliary mass element in the performance of tuned inerter devices. Furthermore, simulations on MDOF structures indicate that the tuned inerter damper, regardless of the presence of an auxiliary mass, outperforms the tuned viscous mass damper at higher modes due to its ability to maintain damping effectiveness at higher frequencies.