In a number of cases, tuned mass dampers (TMDs) have been found to be an appropriate method to suppress vibrations in buildings, floors, sports arena, and other structures. The method is most effective for structures with low damping. Essentially, passively damped oscillators are added to the structure, and tuned to maximize the damping for the modes of the coupled structure-TMD system. By ensuring that the critical modes involve strong participation of the TMD, it is possible to achieve substantial amounts of damping for the coupled system, even if the mass of the TMD is only a small fraction of that of the structure. It is proposed to develop a general methodology for optimum tuning of the TMDs. More precisely, this methodology will yield optimum values of the spring stiffnesses and damping coefficients of the TMD's for given TMD masses and locations. The effects modal interaction will be included, yet the approach is simple enough to be accessible to practicing engineers. An additional advantage of the proposed method is that it only requires a very concise description of the dynamic properties of the structure. This description can for the most part be obtained from field vibration measurements.
