Finding optimal locations of dampers in active controlled structures subjected to earthquakes

Using active dampers for improving structural behavior under earthquakes was widely investigated during the recent years. It was shown that active dampers are very effective and yield significant reductions in response of structures to earthquakes. An important economical issue in design of structures with active control systems is how many dampers should be used. The cost of the control system usually depends on the number and price of a damping unit and its connection to the frame and energy required for activation of the control system to realize the optimal control algorithm. A solution of this problem was proposed by the authors previously. It is based on the modified LQG design of active dampers located at each floor with restrictions of the peak control forces. Energy, dissipated in the dampers, is obtained and most effective dampers' locations are selected according to maximum contribution to the total energy dissipation. This study shows how effective is a limited set of dampers, compared to a full set, when devices are located at all floors. Effectiveness of the proposed method is demonstrated in numerical example. Response of the structures was obtained for full and limited sets of dampers. A criterion, demonstrating the efficiency of a control system with limited set of dampers is proposed. The results of this study form a way for selection of number of dampers and their location allowing effective improvement of structural seismic response.