of an investigation on the dynamics of a small nonlinear oscillator weakly coupled with a linear oscillator were presented. This investigation focused on hysteretic nonlinearity using a Bouc-Wen differential model. It was shown that the absorber can act as an energy sink when it is properly designed; in particular it appears that the level of nonlinearity and the level of damping are important factor for the efficiency of the device. In order to derive approximate solutions to the nonlinear problem, an averaging strategy was used. Investigations of the free and forced responses are presented and, in both cases, it appears that when the energy of the system is sufficient some localization of the vibratory energy in the nonlinear absorber appears. With the examples presented in this paper, we have seen that the nonlinear modes were representative of the behaviour of nonlinear dissipative system in free response as in forced response.

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A. F. Vakakis, O. Gendelman, Energy pumping in nonlinear mechanical oscillators: Part II – Resonance capture, Journal of Applied Mechanics 68 (1) (2001) 42–48.

A. F. Vakakis, L. I. Manevitch, O. Gendelman, L. Bergman, Dynamics of linear discrete systems connected to local, essentially non-linear attachments, Journal of Sound and 