Damage-based design of multiple tuned mass dampers to improve the seismic performance of steel frame structures

Tuned mass dampers are robust tools that can control the undesired vibrations induced by wind and earthquakes. Although vibration control systems such as tuned mass dampers have been used many times by researchers to reduce roof displacement, story drift ratio, and roof acceleration, no research has been reported regarding the reduction of damage's value in the structure. Therefore, in this paper, a three-bay ten-story steel frame building is modeled using the OpenSees software. The building is excited by an earthquake. The Park-Ang damage index is utilized here as an objective function to determine the optimum TMD numbers and parameters. The optimal numbers and properties of TMD systems are calculated by a hybrid binary and real-coded particle swarm optimization (PSO) algorithm. The results indicate the ability of multiple tuned mass dampers to reduce the overall damage and damage stories' values. The results show that this objective function also decreases the maximum drift ratio, residual displacements, and roof displacements. It will lead to improving the seismic performance of the structure. Also, the results show that the damage values are distributed uniformly along with the structure's height by selecting the appropriate domain for the value of the story's damage. A comparison between the proposed method and the Den-Hartog method shows that the proposed method's ability to improve the structure's seismic performance is greater than the classical methods. It can also be concluded from the results that by optimally adjusting the parameters of the control system, the residual displacement of the roof and the displacement of the roof have been reduced by 68.91% and 66.01%, respectively.