Localization of Free Vibration Modes in Systems of Nearly Identical Vibration Absorbers

We demonstrate that the phenomenon of mode localization occurs in the linear free vibration of systems in which multiple, nearly identi-cal vibration absorbers are employed. In these systems the absorbers are not directly coupled to one another via flexibility elements, but rather the coupling is through the inertia of the primary system. The coupling strength in this case is the ratio of the total absorbers ’ iner-tia to the primary mass inertia, and is typically small in applications. A standard eigenvalue/eigenvector perturbation technique is used to find approximations of the modes of free vibration, and it is shown to be accurate when the ratio of coupling to mistuning is small. Both translational and torsional absorber systems are considered, and the results obtained raise some interesting questions regarding the steady-state response of the overall system, and the performance limits of the overall absorber system, when it is subjected to periodic excitation at a frequency close to absorbers ’ frequencies. 1