Optimum tuning of Tuned Mass Dampers for frame structures under earthquake excitation

Tuned Mass Damper (TMD) devices are one of the oldest vibration control means and are widely used in different engineering contexts. Despite the bulk of literature on various TMD-related issues, the effectiveness of TMDs in reducing the earthquake response of civil engineering structures is still debated. This paper deals with the optimum tuning of the free parameters of a passive TMD applied to sample frame structures subjected to selected seismic excitations. A tuning procedure consisting of a numerical Minimax optimization algorithm is implemented within MATLAB. The so-conceived TMD turns out to be optimum with respect to the specific seismic event, hence allowing for optimum reduction in primary seismic response. Both optimization process and seismic analysis are carried out in the time domain, through direct integration of the equations of motion. The method is tested on benchmark single-DOF and multi-DOF shear-type prototype structures from the literature by assuming first the Imperial Valley 1940 seismic input, as a sort of benchmark excitation, and then additional recent strong motion earthquakes. In essence, this paper shows that, in principle, with present reference to frame structures, the optimum tuning of TMD parameters at given seismic input is theoretically possible.