Numerical tuning of Tuned Mass Dampers under earthquake loading

Tuned Mass Dampers are one of the oldest vibration control devices and are widely used in mechanical and civil engineering applications. Despite the bulk of literature available on various TMD-related issues, the effectiveness of TMD devices in reducing the earthquake response of civil engineering structures is still an open research topic. This paper deals with the optimal tuning of the free parameters of a passive TMD applied to sample frame structures subjected to a selected seismic excitation. A tuning procedure consisting of a numerical Minimax algorithm is implemented within a MATLAB environment. The so-conceived TMD turns-out optimal with respect to the specific seismic event, hence allowing for the best reduction in seismic response. Both optimization process and seismic analysis are carried-out in time domain, through direct integration of the equations of motion. The method is tested on benchmark single- and multi-degree-of-freedom shear-type prototype structures from the literature. The average (RMS) displacement of the top storey is taken as objective function; this choice ensures effective convergence and allows for best performance all over the time window of the seismic event. The obtained numerical results are presented in the form of plots and tables. Plots of the trends of the optimal TMD parameters as a function of mass ratio are reported, with comparison to known tuning proposals. Further plots are dedicated to the representation of various response quantities in time. Tables and bar charts report explicitly on the seismic response reduction, as measured by several response indicators, in terms of both kinematic quantities and energy indexes. In essence, this paper shows that, in principle, with present reference to frame structures, the optimal tuning of TMD parameters at given seismic input is possible. This would mean that the TMD could be adopted as a useful control device in such an ideal case. These findings should have important implications in the context of adaptive, semi-active and active TMDs.