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In this work, the reliability and robustness of a nonlinear energy sink device concept are investigated. The system is studied and optimized in deterministic and probabilistic cases. It is also studied under various types of uncertainty modelings with different reliability based robust design optimization formulations. The obtained results reveal the sensitivity of the device to the input uncertainties. The optimal designs obtained with the formulation under uncertainties are very different from the deterministic optimal design. New system configurations are obtained which ensure robust, highly reliable designs. In addition, a comparison is made between the different formulations and a conclusion is drawn about the suitable formulations for such a problem.

In this work, we study the effect of uncertainties modeling and the choice of objective function on the results of optimization design problems in deterministic and probabilistic contexts. Uncertainties modeling are studied in two cases identified in the literature. The results show how the choice of two different objective functions, which lead to the same results in deterministic case, may lead to opposite results in probabilistic case. Also, the results show how the uncertainties modeling type can affect the antagonism between mean and standard deviation in the reliability-based robust design optimization (RBRDO) problems. Three mechanical applications chosen from the literature are used to illustrate these cases.