Optimum parameters and performance of negative stiffness and inerter based dampers for base-isolated structures

Novel combinations of true negative stiffness dampers (NSDs) and inerter devices are used concurrently as supplemental dampers for response control of base-isolated structures. The combination of the inerter and NSD is denoted as negative stiffness inerter damper (NSID). Classical H∞ optimisation based on a well-known fixed-point theory of tuned mass dampers is used to derive optimal parameters for NSD and three configurations of NSIDs. Optimal NSIDs and NSD are supplemented to the base-isolated structure as passive control devices. The closed-form expressions for optimal parameters are derived, which will be useful for the initial design process of these devices for isolated structures. A numerical searching technique is used to verify the derived closed-form expressions for the optimal parameters of NSIDs. A comparative analysis is also run by utilising three configurations of NSIDs and a true NSD as supplemental control devices to the flexible base-isolated structure. The governing equations of motion are written in state-space form, and the performance of the proposed supplemental dampers for the base-isolated structure is investigated under real earthquake records. Time history analysis shows that the optimal NSIDs and NSD effectively control the objective variables of base displacement, inter-storey drift, and top storey acceleration. Especially under near-fault, which may bring isolation systems to critical working conditions, the proposed supplemental dampers cushion against failure by improving energy dissipation capacity compared to conventional passive dampers. Optimal NSID parameters are lower in magnitude than NSD parameters, resulting in a smaller damper size, which is desirable from a practical design standpoint.