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The present investigation deals with the dynamics of a two-degrees-of-freedomsystem which consists of a main linear oscillator and a strongly nonlinearabsorber with small mass. The nonlinear oscillator has a softening hystereticcharacteristic represented by a Bouc-Wen model. The periodic solutions of thissystem are studied and their calcu- lation is performed through an averagingprocedure. The study of nonlinear modes and their stability shows, underspecific conditions, the existence of localization which is responsible for apassive irreversible energy transfer from the linear oscillator to thenonlinear one. The dissipative effect of the nonlinearity appears to play animportant role in the energy transfer phenomenon and some design criteria canbe drawn regarding this parameter among others to optimize this energytransfer. The free transient response is investigated and it is shown that theenergy transfer appears when the energy input is sufficient in accordance withthe predictions from the nonlinear modes. Finally, the steady-state forcedresponse of the system is investigated. When the input of energy is sufficient,the resonant response (close to nonlinear modes) experiences localization ofthe vibrations in the nonlinear absorber and jump phenomena.

Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber