DYNAMIC CHARACTERIZATION OF MULTIPLE TUNED MASS DAMPERS AND SOME DESIGN FORMULAS

Multiple Tuned Mass Dampers (MTMD) consist of a large number of small oscillators with natural frequencies distributed around the natural frequency of a controlled mode of the structure. In the present paper, the modal characteristics and efficiency of the MTMD are studied analytically. Perturbation solutions for the modal properties of the MTMD-structure system are obtained and the modal characteristics are discussed. An explicit formula to estimate the effectiveness of the MTMD subjected to harmonic forces is also derived. It is shown that the MTMD is efficient when at least one of the oscillators is strongly coupled with the structure in any mode. Based on this observation, a critical bandwidth of the natural frequencies of the MTMD to make the system multiply tuned is derived in a simple form, and furthermore a robustness criterion for the frequency tuning under a given bandwidth is proposed. It is shown that, when properly designed, the MTMD can be much more stable (robust) than a conventional single TMD while maintaining more or less the same efficiency. Numerical studies verify the accuracy of the perturbation solutions and the proposed formulas: