Summary: This paper explores the influence of linear hysteretic damping on the performance of passive tuned‐inerter devices. An inerter is a device that produces a force proportional to the relative acceleration across its two terminals; devices incorporating inerters have received widespread attention in the earthquake engineering community, because they offer the ability to improve the seismic response of structures. However, the majority of this research has assumed that the damping components within the tuned‐inerter device exhibit viscous, rather than hysteretic, damping. This restriction imposes an essential question on how the hysteretic damping model will change the performance of the device compared with the viscous damping model. It is shown that the response of viscous and hysteretic inerter systems have significant differences in displacement amplitude due to the frequency dependency of the damping. Therefore, a new formulation for obtaining the optimum loss factor of the hysteretic damping in the inerter system is proposed. Next, the challenges associated with accurately predicting the time‐response of a hysteretically damped system are discussed. A numerical time‐integration method is extended to address these challenges, using a new formulation that has the benefit of being broadly applicable to multidegree‐of‐freedom hysteretic linear systems and nonstationary random signals. The results show that the earthquake responses from the hysteretic damping model can differ significantly from the ones obtained via the viscous model.

An inerter is a mechanical analogue to a capacitor, where the force across the device is proportional to relative, rather than absolute, acceleration. This concept can offer attractive performance in a wide variety of engineering vibration problems, because the engineer can tune the device without dramatically increasing the physical mass of the structure. Consequently, there have been many studies over the last two decades that have explored their application to bridge vibrations, seismic isolation of tall buildings, vehicle suspensions, and other engineering problems. Several configurations of inerter systems have been proposed, typically involving the inerter in a vibration absorber, or by using the inerter as part of an isolation system. However, to date there have been limited studies that have explored the combination of inerters with semi-active devices such as magnetorheological fluid dampers. Furthermore, because one manifestation of inerters involves the use of hydraulic fluid, it is possible for magnetorheological effects to be integrated into the inerter itself. The present study investigates the feasibility of this approach for practical scenarios. A quasi-static model is developed, combining an existing model of a fluid inerter with simplified models for magnetorheological fluids. The trade-off between damping performance and inerter performance is explored. The model is then used in a case study, where its potential use in a control strategy known as a parallel-layout inerter damper is investigated.