Exact H2 optimal solutions to inerter-based isolation systems for building structures

This paper presents two inerter-based isolation systems, namely, an inerter-damper (ID)-based isolation with an inerter in parallel with a viscous damper and a tuned ID (TID)-based isolation composed of an inerter in series with a spring-damper pair. A base-isolated building with two degrees of freedom (DOF) is considered, where the superstructure above the base is simplified as a single DOF. The H-2 norm performances of the ID- and TID-based isolation systems are introduced in comparison with the traditional isolation system, with the aim to minimize structure damage under random excitation from ground acceleration. The closed-form solutions are obtained, including the damping ratio of the traditional isolation, the damping ratio and the inertance-to-mass ratio of the ID-based isolation, and the damping ratio and inerter frequency tuning ratio of the TID-based isolation. It is shown that the TID-based isolation is superior to both the traditional and ID-based isolation systems for vibration control. Specifically, the optimal H-2 norm of the transmission from the ground acceleration to the building relative displacement in the TID-based isolation can be reduced by 7.5%. The influence of the primary damping of the building structures is also studied numerically, in both the frequency and time domains, and compared with the exact optimal solution of the undamped structure. The simulations using recorded earthquake spectra show that the ID- and TID-based isolations can further reduce the story drift, the base displacement as much as 48.5% and 66.3% (root mean square) and 37.8% and 71.9% (peak) for the El Centro record compared with the traditional isolation system.