  Many engineering structures are composed of weakly coupled sectors assembled
in a cyclic and ideally symmetric configuration, which can be simplified as
forced Duffing oscillators. In this paper, we study the emergence of localized
states in the weakly nonlinear regime. We show that multiple spatially
localized solutions may exist, and the resulting bifurcation diagram strongly
resembles the snaking pattern observed in a variety of fields in physics, such
as optics and fluid dynamics. Moreover, in the transition from the linear to
the nonlinear behaviour isolated branches of solutions are identified.
Localization is caused by the hardening effect introduced by the nonlinear
stiffness, and occurs at large excitation levels. Contrary to the case of
mistuning, the presented localization mechanism is triggered by the
nonlinearities and arises in perfectly homogeneous systems.
