Reliability of multiple tuned mass dampers for bridge flutter control

A probabilistic framework for the optimal design of irregular multiple tuned mass dampers (MTMDs) for bridge flutter control is established, with a particular care to the reliability of the devices. The outcome of the design process is the definition of the parameters of the passive devices that meet some specified robustness requirements against frequency mistuning and maximize the percentage increment of a properly defined characteristic value of the critic flutter velocity. This last is indeed modeled as a random variable, being a deterministic function of uncertain aeroelastic derivatives and structural parameters. A practical case study is considered to validate the proposed approach. The aeroelastic stability analysis is performed in the time domain via the solution of a direct eigenvalue problem, by representing the aeroelastic loads through indicial functions and by evaluating structural mode shapes and natural frequencies by means of a finite element model of the bridge. The results show the feasibility of the proposed design approach and outline that a special class of irregular MTMDs, obtained though an unequal mass distribution, allows to improve the reliability of the passive device with respect to regular MTMDs.