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27 June 2002 Design of multi-degree-of-freedom tuned-mass dampers
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Many methods have been developed for the design of a single-degree-of-freedom (SDOF) vibration absorber to damp SDOF vibration since Den Hartog presented his fixed points method in 1928. But a rigid body employed as a vibration absorber will in general have six degrees of freedom relative to a structure. By taking full advantage of the inertia of the body, we can damp as many as six modes, or make the system more robust or compact. In this paper, we present a two-step method for optimization of the stiffness and damping of a multi-degree-of-freedom connection between a reaction mass and a vibrating structure: First, treating the reaction mass as a perturbation to the vibrating structure, we obtain an approximate design. Second, we adapt a descent-subgradient method to fine-tune the design by maximizing the minimal damping over a prescribed frequency range.
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Jusin M. Verdirame, Samir A. Nayfeh, and Lei Zuo "Design of multi-degree-of-freedom tuned-mass dampers", Proc. SPIE 4697, Smart Structures and Materials 2002: Damping and Isolation, (27 June 2002);

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