Comparison on different approaches for robust optimum design of tuned mass dampers

This study investigates the effects of structural uncertainties on design and performance evaluation of passive tuned mass dampers (TMD) used for vibration control. A robust optimal design methodology is presented in which are assumed timeinvariant uncertain structural parameters. Unlike conventional TMD designs, based on the implicit assumption that all parameters involved are deterministically known, a robust approach is considered in the proposed design which properly accounts for uncertainties in load and structural models. In comparison to a conventional method, the solution must be able not only to minimize a performance but also to limit its variation induced by uncertainty in system parameters. The importance of structural uncertainties is demonstrated by applying the methodology to a single degree of freedom structure subjected to a stationary white noise. The problem is treated characterising all uncertain parameters by a nominal mean value and a variance. It is also assumed that all these parameters are statistically independent. Three kinds of methods are compared: the single-objective conventional optimization and the single and the multi-objectives robust optimization ones. With reference to this last, a Pareto evolutionary algorithm is used to identify a number of optimal solutions that are distributed along the Pareto front. It is found that the consideration of structural uncertainties improves substantially the robustness of the TMD design. Also, multi-objective robust TMD-design methodology induces a significant improvement in performance stability and furnishes a better control on the design solution chosen.