Minimax optimization of Tuned Mass Dampers under seismic excitation

The present paper concerns the optimal tuning of the free parameters of passive Tuned Mass Damper (TMD) devices, added to benchmark frame structures taken from the literature and subjected to a given deterministic seismic excitation. The tuning procedure is achieved through a numerical optimization approach, namely a Minimax algorithm implemented in a MATLAB environment. Different objective functions have been considered, from both kinematic and energy response indicators of the primary structure. The optimization process is carried-out in time domain, whereby the dynamic response is evaluated numerically by a step-by-step integration based on Newmark's average acceleration method. In order to assess the efficiency of the proposed methodology and investigate the effectiveness of the so-conceived TMD, several numerical tests on both single-and multi-degree-of-freedom frame structures endowed with a TMD are performed. The salient numerical results are presented in plots and tables. Plots of the optimal TMD parameters (frequency ratio and damping ratio) as a function of mass ratio are reported and graphs showing the seismic response reduction in terms of top-floor displacement are provided. Tables gathering the optimal TMD parameters and the seismic response reduction at assumed given values of the mass ratio are outlined. Comparisons to results obtained from well-known tuning formulas are provided. The achieved output demonstrates the reliability of the proposed method and shows that, in principle, the design of an optimal TMD device for a specific seismic event is possible. This should have important implications in the framework of adaptive, semi-active and active TMD devices.