Optimum vertical location and design of multiple tuned mass dampers under seismic excitations

An efficient optimum vertical location and design method of multiple tuned mass dampers (MTMDs) is proposed in order to reduce the response of building structures under seismic excitation. Governing equations are derived in frequency domain in terms of random vibration theory and probabilistic critical excitation method. In order to determine the location and optimum parameters of each tuned mass damper (TMD) which are mass, stiffness and damping coefficient, both top storey mean square absolute acceleration and displacement of shear building are chosen as the objective functions to be minimized via Differential Evolution (DE) optimization method. It is assumed that there is one TMD on each storey at the initial stage of the method. During the optimization, if the mass or stiffness parameters convergence to zero on a specific storey, then TMD is eliminated, so that optimum placement can be achieved. The sum of the critical effects corresponding to the selected bandwidths in the first, second and third frequency peak regions of the structure is taken into account, thus the high mode behaviors are also controlled. In order to understand the performance of proposed method, shear building model with multiple TMD is tested using different earthquake acceleration records and the findings are compared with some other studies available in the literature. The results show that the optimal MTMD design obtained from proposed method is very effective in reducing the dynamic response of building structure.