Optimum design and performance of a base-isolated structure with tuned mass negative stiffness inerter damper

In order to increase the efficiency of the structures to resist seismic excitation, combinations of inerter, negative stiffness, and tuned mass damper are used. In the present work, the optimum tuning frequency ratio and damping of the tuned mass negative stiffness damper-inerter (TMNSDI) for the base-isolated structure were determined by employing the numerical searching technique under filtered white-noise earthquake excitation and stationary white noise. The energy dissipation index, the absolute acceleration, and the relative displacement of the isolated structure were considered as the optimum parameters, obtained by their maximization. Evaluations of base-isolated structures with and without TMNSDI under non-stationary seismic excitations were investigated. The efficiency of the optimally designed TMNSDI for isolated flexible structures in controlling seismic responses (pulse-type, and real earthquakes) were evaluated in terms of acceleration and displacement. A dynamic system was used for deriving the tuning frequency and tuned mass negative stiffness damper inerter (TMNSDI) for white noise excitation by using explicit formulae of the curve fitting method. The proposed empirical expressions, for design of base-isolated structures with supplementary TMNSDI, showed lesser error. Fragility curve results and story drift ratio indicate reduction in seismic response by 40% and 70% in base-isolated structure using TMNSDI.