Multi-objective optimal design of tuned mass dampers

This paper first presents a multi-objective optimization problem formulation for the design of a tuned mass damper (TMD) for either a base excitation or an external load. The optimization seeks to simultaneously minimize structural responses, the TMD mass and the TMD stroke. A white noise input is adopted to represent the base acceleration or the external load. Alternatively, a filtered white noise could be used. Furthermore, the TMD is assumed to be tuned to dampen one of the modes of the structure, typically the first mode. Two approaches for the solution of the problem are then presented. The first approach directly solves the problem while considering the full multi-degree-of-freedom system and the TMD equations. Using the second approach, the multimodal response of the structure is first approximately decomposed to its modal contributions. The modal contribution of the damped mode could thus be analyzed as a single-degree-of-freedom system with a TMD. An intensive parametric study, where the response of a single-degree-of-freedom system equipped with a TMD is optimized in a multi-objective sense, is then performed. This parametric study enables gaining insight to the behavior of the problem. Furthermore, its results assist in executing the second optimization approach without having to actually run the optimization algorithm. The second approach is also implemented in an Excel spreadsheet that is attached as Supporting Information.