Optimal design of a novel tuned inerter damper system for reducing the displacement demand of base-isolated structures

Among the passive vibration control strategies in civil engineering, seismic base isolation is nowadays extensively adopted to protect structures against destructive earthquakes. By providing flexibility at the base of the structure, most of the earthquake-induced displacement demand is concentrated at the isolation level, thereby the base-isolation system undergoes large displacements. In an attempt to reduce such displacement demand, this paper proposes an enhanced base-isolation system incorporating the inerter, a two-terminal flywheel device whose generated force is proportional to the relative acceleration between its terminals. The inerter acts as an additional, apparent mass that can be orders of magnitude higher than its physical mass. When the inerter is installed in series with spring and damper elements, a lower-mass and more effective alternative to the traditional tuned-mass-damper (TMD) is obtained, i.e., the tuned-inerter-damper (TID) wherein the device inertance plays the role of the TMD mass. By attaching a TID to the isolation floor, the displacement demand of base-isolated structures can be significantly reduced. To this aim, we determine the optimal parameters of the TID system that minimize the displacement demand of base isolated structures. Due to the stochastic nature of the earthquake input, optimal design of the TID is based on a probabilistic framework. Different optimization procedures are scrutinized on the basis of the covariance matrix of the system response. The effectiveness of the optimal TID parameters is assessed via timehistory analyses of base-isolated multi-story buildings under several earthquake excitations. It is demonstrated that the proposed enhanced base-isolation system attains an excellent level of vibration reduction as compared to the conventional base-isolation scheme, in terms not only of displacement demand of the isolation system, but also of response of the isolated superstructure (e.g., base shear, interstory drifts); moreover, it does not imply excessive stroke of the TID.