Nonlinear energy channeling in the two-dimensional, locally resonant, unit-cell model. I. High energy pulsations and routes to energy localization.

Abstract

Present paper is the first one in the series devoted to the analytical investigation of energy channeling phenomena emerging in the locally resonant unit-cell model comprising an outer mass incorporating internal rotator and subject to the 2D, nonlinear local potential. In the current study, we mainly focus on the analysis of the mechanisms of formation and bifurcations of the special type of non-stationary regimes, characterized by the massive, bidirectional energy transport between the axial and the lateral vibrations of the outer element controlled by the internal, rotational device as well as the regimes of the unidirectional energy localization. The devised analytical procedure is based on a singular multi-scale analysis constructed for the special asymptotic limit corresponding to the high energy excitations. The basic question of possible coexistence of various stationary and non-stationary system regimes as well as their local and global bifurcations is addressed via the reduction of the global flow on the slow invariant manifold in the vicinity of the fundamental resonance. Numerical simulations fully confirm the analytical predictions concerning the structure of the response regimes and their bifurcations.