The Multi-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation∗

Formulas for the optimal design of single-degree-of-freedom (SDOF) tuned-mass dampers (or dynamic vibration absorbers) for SDOF structures under random and harmonic excitations have been available for many years. Whenever an absorber body is attached to a primary system, there is potential for utilization of motion in more than one degree of freedom of the body relative to the primary system. In this paper, we propose that more than one mode of vibration of a body relative to a primary structure be tuned to one natural frequency of a primary system. We cast the problem of optimizing the multidegree-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∞ norms to minimize the response to random and harmonic excitations, respectively. We perform a detailed study of the two-degree-of-freedom absorber and provide charts of optimal parameters ready for use in design. We show that 2DOF ∗draft for 2003 ASME Design Engineering Technical Conferences