Present study is devoted to a detailed investigation of energy channeling phenomena emerging in the, unit-cell model. The model under consideration comprises an outer mass incorporating internal rotator and mounted on the 2D, nonlinear elastic foundation. The first part of the work is devoted to the analytical and numerical study of various response regimes exhibited by the system under consideration ranging from simple periodic and up to strongly modulated ones for the low energy level of initial excitation. The devised analytical procedure is based on a regular multi-scale expansion constructed for the limit of low energy excitations. Special emphasis is given to the description of intrinsic mechanisms leading to a complete, unidirectional energy channeling from axial to lateral vibrations.
The second part of the work focuses on the analytical description of the intrinsic mechanisms governing the formation of high energy pulsations (i.e. complete, recurrent energy transport) between the axial and the lateral vibrations altered by the spontaneous unidirectional energy localization. The devised analytical procedure is based on a singular multi-scale analysis constructed for the special asymptotic limit of high energy excitations. The basic question of possible coexistence of various system regimes such as simple periodic, (weakly and strongly) pulsating as well as the unidirectionally localized ones is addressed via the reduction of the global flow on invariant manifold (SIM) in the vicinity of the fundamental resonance (1:1:1). Numerical simulations fully confirm the analytical predictions concerning the structure of the response regimes and reveal their peculiar local and global bifurcations.
