The need for larger and more efficient structures has led to the development of numerical models to approach real-world complex behaviors. Normally, engineering systems consider deterministic parameters, while in real-world situations, they are subjected to parametric uncertainties, resulting in differences between the calculated responses. This work is devoted to performing numerical and computational studies of fatigue damage analyses of viscoelastically damped systems in the frequency domain subjected to parametric uncertainties. Here, the discretization of the random field is performed using the finite element method combined with the Karhunen-Loève expansion and the fatigue damage index is estimated by applying the so-called Sines' global criterion. Optimization techniques were applied in order to obtain the optimal design of surface viscoelastic treatments in terms of fatigue. Therefore, the main contribution intended for the present study is to show the importance of considering optimal-robust parameters to estimate the failure probability of engineering structures with constrained viscoelastic layers. After presenting the underlying foundations, the numerical results are presented and the main features of the proposed methodology are highlighted.

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materials, hydrodynamic and magnetic bearings, and smart rotating machines. The financial support of the official agencies CNPq, CAPES, and FAPEMIG are highly appreciated. Finally, it is worth mentioning that a significant part of the work conveyed has been developed with the participation of the industry. In this context, the authors are thankful to the financial support provided by the companies Embraer and Petrobrás. In particular, the authors are thankful to CERAN, BAESA, ENERCAN, CPFL Energia, and Foz do Chapecó for the financial support through the R&D project Robust Modeling for the Diagnosis of Defects in Generating Units (ANEEL 02476-3108/2016).