On the optimal design and robustness of spatially distributed tuned mass dampers. (March 2021) - Americano da Costa, Mariana M.; Castello, Daniel A.; Magluta, Carlos; Roitman, Ney
Highlights: An approach to optimally design "spatially distributed" tuned mass dampers. The hypothesis of uniform modal damping ratios is amenable for d-MTMD design. Sensitivity analyses regarding the impact of the main system and d-MTMD on the effectiveness. A map from the level of model uncertainties onto the robustness of the optimum solution. Abstract: Tuned-Mass-Dampers (TMD) have been widely used to suppress undesirable structural vibrations within a user-defined frequency band. Nevertheless, the performance of TMDs designs is quite sensitive to slight deviations in model parameters such as the ratio between the TMDs natural frequency and the frequency of the main structure. This paper proposes (i) a systematic approach to design a set of spatially distributed TMDs aiming at minimizing the system response when upper bounds for damping ratios should be taken into account and (ii) a straightforward way to analyze the level of robustness of the optimum design under different levels of model uncertainties. Some numerical results are presented considering the design of a set of spatially distributed TMDs to be placed over a rectangular plate with non-ideal boundary conditions. The optimum solution is determined by means of an optimization algorithm and the robustness of the optimum solution is computed by means of Monte Carlo Simulation analyses. The analyses consider that uncertainties may come from TMD model parameters, from plate model parameters and from both of them simultaneously. These analyses allow one to build a design chart from which one may obtain the robustness of the optimum solution as a function of model uncertainties. Finally, robustness assessment in time domain is performed considering a random excitation along with model parameter uncertainties.