Optimization of three-element tuned mass damper based on minimization of the acceleration transfer function for seismically excited structures

The three-element tuned mass damper (T-TMD) is an effective passive control device for single-degree of freedom structures due to harmonic external force. Unlike previous studies, this study aims at proposing a methodology for optimization of T-TMD positioned at the top floor of multi-degree of freedom structures under seismic loads. The equations of motion for a multi-story building controlled by a T-TMD are derived, and the T-TMD is then optimized using an advanced firefly algorithm (AFA) in the frequency domain. The aim of the optimization is to minimize the amplitude of the acceleration transfer function of the top floor of the building. The proposed methodology is implemented in two different shear buildings, and the optimum parameters are then verified by using benchmark earthquakes with different frequency components. The comparisons with the available works illustrate the availability of the AFA. The effect of the mass ratio on the optimum parameters of the T-TMD is also discussed in detail. Numerical results show that the use of the optimum T-TMD is an effective strategy to minimize the maximum structural responses of the multi-story buildings under seismic excitations. In particular, the optimum T-TMD is very effective when the maximum story responses (i.e., displacement and acceleration) occur at the top floor of the building.