Robust optimization of MTMD systems for the control of vibrations

Multiple Tuned Mass Dampers (MTMD) is one of the simplest and most reliable solution to control the vibrations of a structure, e.g. allowing to deal with a wide distribution of structural natural frequencies and usually showing inherent stability. Nevertheless, uncertainties in the behavior of structures under random dynamic input may induce implications on the MTMD effectiveness, e.g. detuning or amplifications. Typically, uncertainties in the input are exclusively considered, while uncertainties affect as much also the mechanical parameters. This paper proposes a robust optimum design of the MTMD, considering uncertainties both in the structural parameters and in the earthquake input. At this aim, a random vibration analysis of the response is adopted, and a direct linear perturbation method is applied on the uncertain parameters. Results show that a deterministic optimization is inappropriate for sensible systems as TMDs, while a robust optimization aims to better control the response with low computational efforts. Furthermore, the selection of the objective functions significantly affects the optimal design parameters, as the number of TMDs influences the robust designs.