Shake table experimental validation of auxiliary mass effects in a tuned viscous mass damper

Inerter-based dampers have received significant attention in the structural engineering community. Among these, the tuned viscous mass damper (TVMD) is the only variant that has been implemented in real-world buildings. The conventional TVMD model comprises an inerter connected in parallel with a dashpot and in series with a spring. However, this simplified model overlooks the influence of the physical mass of the device itself, which includes the moving components between the inerter and spring. In this paper, the device’s physical mass, whether explicitly accounted for or intentionally added to enhance its performance, is referred to as an auxiliary mass. The device configuration of the TVMD with an auxiliary mass is the same as that of a novel tuned mass damper inerter (NTMDI) reported in the literature. However, optimal design formulae that minimise the $H_{\infty }$ norms of the transfer function from ground displacement to floor displacement relative to the ground are lacking. These shortcomings are addressed in this study. Furthermore, shake table tests were conducted on a scaled single-storey steel specimen containing an NTMDI. The device features a flywheel with permanent magnets and is connected to the structural mass via leaf springs. The experimental results demonstrate that the auxiliary mass significantly improves the dynamic performance of the TVMD.