Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of 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 suppress single-mode vibration of a primary system. We cast the problem of optimization of 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 zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.
The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation
Zuo, L., and Nayfeh, S. A. (April 1, 2005). "The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation." ASME. J. Vib. Acoust. February 2006; 128(1): 56–65. https://doi.org/10.1115/1.2128639
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