Results on discrete [@Vakakis-JSV03; @Gendelman-JSV-2005] and continuous systems [@Mikhlin-JSV] were presented and in most of studies, the nonlinear absorber consisted in an essential cubic nonlinearity. Several methodologies where investigated and developed to study this phenomenon. The use of asymptotic techniques to find approximate solutions was addressed in several works; Vakakis [*et al. *]{} [@Vakakis-JSV03] used an averaging method, Gendelman [*et al.*]{} [@Gendelman-JSV-2005] used a multiple scale method, Mikhlin and Reshetnikova [@Mikhlin-JSV] used an expansion method in combining with a Mathieu equation comparison to investigate the stability of periodic solutions…Moreover Vakakis and Rand [@Vakakis-Rand2004] proposed a method to derive exact solutions for systems with cubic nonlinearities based on the use of elliptic functions. Experimental results were also presented [@Vakakis-NLM-exp; @Pernot-Exp] in which the nonlinear device is made of a geometric nonlinearity. Applications have been proposed in shock isolation or in civil engineering.

A common result to explain this phenomenon is that, under specific conditions, some localization of the vibratory can occur leading to an irreversible passive transfer of the energy from the linear structure to the absorber. This result was demonstrated using the stability of the periodic solutions; Vakakis [@Vakakis-AppliedMech1; @Vakakis-AppliedMech2] provided a theoretical background on the subject studying periodic orbits 