A firefly algorithm for the design of force and placement of friction dampers for control of man-induced vibrations in footbridges

It is known that the use of passive energy dissipation devices, as friction dampers, reduces significantly the dynamic response of structures subjected to dynamic actions. However, the parameters of each damper as well as the best placement of these devices remain difficult to determine. Although some studies on optimization of tuned mass damper and viscous/viscoelastic dampers are being developed, works on optimum use of friction dampers is still lacking. Thus, in this paper, the simultaneous optimization of force and placement of friction dampers is proposed. To solve this optimization problem, the recently developed firefly algorithm is employed, which is able to deal with non-convex optimization problems, involving mixed discrete and continuous variables. For illustration purposes, two common footbridges are analyzed, in which the cost function is to minimize the maximum acceleration of the structures, whereas forces and positions of friction dampers are the design variables. The results showed that the proposed method was able to determine the optimum friction forces of each damper as well as their best positions in the structures. The maximum acceleration was reduced in more than 95 % for the Warren truss footbridge, with three friction dampers, and in more than 92 % for the Pratt truss footbridge, with only two friction dampers. In addition, the proposed methodology is quite general and it is believed that it can be recommended as an effective tool for optimum design of friction dampers for structural response control. Thus, this paper shows that the design of friction dampers can be done in a safe and economic way.