Whenever a tuned-mass damper is attached to a primary system, there is potential for utilization of motion of the absorber body in more than one degree of freedom relative to the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to a single natural frequency of the primary system. We cast the problem of optimizing the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem, and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to be zero. With properly chosen connection locations, the two-DOF absorber can achieve better vibration suppression than two separate absorbers of optimized mass distribution. We also find that a two-DOF absorber with negative dampers in some of the connections to the primary system can obtain much better performance than absorbers with only positive dampers.
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