Feasibility of an inerter-based causal rate-independent damping model for the protection of seismically isolated structures

Rate-independent linear damping (RILD), also referred to as linear hysteretic damping, is a linear model of structural or material damping in which the energy dissipation per cycle is independent of the frequency. The resistive force of an ideal RILD model is in phase with the velocity to dissipate energy, while its amplitude is proportional to the displacement, which is suitable for the direct control of seismic response displacement when incorporated into a structure. The tuned Maxwell–Wiechert (TMW) model is a viable option for approximating the damping characteristics of RILD. However, the undesirable stiffness produced by the TMW model compromises the flexibility of the isolator, and thereby fails to deliver the benefits of RILD. To overcome this challenge, the addition of two inerter elements to the TMW model in series and parallel arrangements is proposed in this study to eliminate the undesirable storage stiffness. The parameters of the proposed model are determined using particle swarm optimization. Analyses of a 10-story building structure mounted on linear and nonlinear isolation systems demonstrated that the proposed model achieved lower interstory drifts and approximately 40% reduction in floor response accelerations, with similar isolator displacements compared with LVD when subjected to ground motions dominated by high-frequency components. Moreover, floor response acceleration mitigation was attained at the slight expense of isolator displacement, even when the proposed system was incorporated into nonlinear isolation systems and subjected to low-frequency ground motions.