Robust optimum design of tuned mass damper devices in random vibrations mitigation

One of the most widely adopted and studied strategies for vibration control both in civil and in mechanical engineering is based on the use of tuned mass dampers (TMD) devices. Many conventional optimization criteria of mechanical parameters have been proposed, based on different approaches typically of a "conventional" type; in other words, they are based on the implicit assumption that all parameters involved are deterministically known. Removing this hypothesis means to convert a conventional optimization into a robust one, so that the solution must be able not only to minimize a performance but also to limit its variation induced by uncertainty in system parameters. In this work, a robust optimal design criterion for a single TMD device is proposed. The analyzed case concerns the structural vibration control of a main system subject to stochastic dynamic loads by a single linear TMD. The dynamic input is represented by a random base acceleration, modelled by a stationary filtered white noise process. It is assumed that not only mechanical parameters regarding main structure and TMD but also input spectral contents are affected by uncertainty. The problem is treated characterizing all uncertain parameters by a nominal mean value and a variance. It is also assumed that all these parameters are statistically independent. The protected main structure covariance displacement (dimensionless by dividing for the unprotected one) is adopted as the deterministic objective function (OF). Its mean and standard deviation are evaluated to perform the robust design. Robustness is formulated as a multiobjective optimization problem, in which both the mean and the standard deviations of the deterministic OF are minimized. Comparisons with a conventional approach based on the same OF show that the robust approach induces a significant improvement in performance stability.