Robust optimum criteria for tuned mass dampers in fuzzy environments

Tuned mass dampers are widely adopted passive strategies for vibrations mitigation, in the past years extensively investigated to improve the offered protection level in any mechanical systems in which they are installed. Although different mechanical and energetic optimum criteria have been proposed in the last decades by assuming involved parameters as deterministically known, nowadays the need persists to explore more realistic approaches for virtue of the unavoidable presence of uncertain variables. In fact, deterministic-based optimum criteria often lead to incorrect design, evidently because it is an excessive oversimplification and heavily in conflict with practical circumstances. Consequently, searching for robustness-based criteria in the optimal design for this class of mechanical devices is a crucial question. In order to define a collection of solutions able to ensure an acceptable trade-off between mechanical performances and immunity against the variability of the involved parameters, robust-based design optimization is an important and alternative way for supporting design process. Typically, methods proposed until now are based on the probabilistic description of the uncertain variables and only few approaches consider uncertainties in both system and loads. In this paper, robust-based design optimization problems for tuned mass dampers are formulated and resolved in view of fuzzy environments. The antithetical objective functions of the problems are defined within the framework of the credibility theory: the first one is the fuzzy expected value of the adopted performance-based structural index, the second one is its fuzzy variance. Specifically, this latter is introduced to characterize the performance variability due to the existence of uncertain variables. In our analysis, protected systems are assumed subject to random vibrations, in the aim to extend the applicability of the proposed methodology to different and general (natural or artificial) dynamic loads. Both models for structural systems and dynamic loads include fuzzy variables, in order to take into account also epistemic uncertainties. Finally, several numerical applications are presented to investigate the practical utility of the obtained results.