Optimal Design of Multiple Tuned Mass Dampers for Seismic Control of an Inelastic Steel Moment-Resisting Frame

The effectiveness and robustness of multiple tuned mass dampers (MTMD) depend on the total number and characteristics of tuned mass damper (TMD) units, and the behavior of structures. This study presents the optimal design of an MTMD system for suppressing the seismic responses of a ten-story inelastic steel moment-resisting frame (SMRF) subjected to an artificial earthquake excitation. The optimal design of the MTMD system is formulated in the framework of an optimization problem with single objective function so that the optimal parameters of TMD units are found for a specified mass ratio of the MTMD system. Two different objective functions including the root mean square of drifts and the cumulative hysteretic energy of the controlled SMRF (as the global damage indices of structures) are selected and minimized. The effectiveness of the optimized MTMD system is also compared with that of the optimized single TMD. It is demonstrated that the optimized MTMD system is more effective than the optimized single TMD in reducing the seismic responses of the inelastic SMRF. In addition, the effectiveness of the optimized MTMD system for the seismic control of the inelastic SMRF remains almost constant beyond a certain number of TMD units. Finally, the performance of the optimized MTMD system is assessed under four real earthquake records and is compared with that of the optimized single TMD. The assessment results indicate that the optimized MTMD system can provide a better control performance than the optimized single TMD.