Optimum Tuned Inerter Damper for Base-Isolated Structures

The optimum damping and tuning frequency ratio of the tuned inerter damper (TID) for the base-isolated structure is obtained using the numerical searching technique under stationary white-noise and filtered white-noise earthquake excitation. The criterion selected for optimality is the minimization of the mean-square relative displacement and absolute acceleration of the isolated structure and maximization of the energy dissipation index. Explicit formulae for TID damping and tuning frequency for white-noise excitation are then derived using a curve-fitting technique that can be conveniently used for applications in dynamical systems. The error in the proposed empirical expressions is found to be negligible and hence these expressions are quite useful for the effective design of the base-isolated structure with supplemental TID. An optimally designed TID was found to be more effective for the base-isolated structures under soft soil conditions in comparison to the firm soils. Further, a comparison of the seismic response of the flexible base-isolated structure with and without TID was made under non-stationary earthquake excitation. It was observed that an optimally designed TID was found to be effective in controlling the displacement and acceleration response of the base-isolated structure and the effectiveness is observed to be increased for a higher inertance mass ratio. Finally, the close form expression for the bearing displacement of base-isolated structure with TID subjected to broadband earthquake excitation is proposed which will be helpful for initial optimal design.