oscillator connected to a small strongly non-linear hysteretic absorber\
International Journal of Non-Linear Mechanics, Volume 41, Issue 8, October 2006, Pages 969-978\
D. Laxalde, F. Thouverez and J.-J. Sinou

[**Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber**]{}

D. Laxalde$^{a,b}$, F. Thouverez$^{a}$, J.-J. Sinou$^{a}$

${}^{(a)}$ Laboratoire de Tribologie et Dynamique des Systèmes (UMR CNRS 5513)\
École Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France\
${}^{(b)}$ Snecma – Safran group, 77550 Moissy-Cramayel, France

#### Keywords:

Hysteresis, nonlinear energy sinks, non-linear modes, averaging method

Introduction
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Vibration control of mechanical systems is of permanent interest in the field of engineering and research. Dissipation or absorption of the unwanted and often dangerous vibratory energy can be achieved by various ways, using passive or active devices, dissipative materials, coatings, visco-elastic materials, tuned mass dampers or friction …

Recently, the interest for nonlinear absorbers kept growing. In particular, several works on vibration control through the use of a small passive strongly nonlinear device have been presented. The concept of [*energy pumping*]{}, that is a passive irreversible one-way energy transfer from a main (linear) structure to a strongly nonlinear (non-linearizable) attachment, was introduced and developed [@Vakakis-AppliedMech2; @Vakakis-JSV03; @Mikhlin-JSV]. 