Three-dimensional energy channeling in the unit-cell model coupled to a spherical rotator II: unidirectional energy channeling

Abstract

This work is the second one in a two-part series devoted to the analysis of complex nonlinear mechanism of energy channeling emerging in a locally resonant three-dimensional, unit-cell model, and the current paper considers unidirectional energy channeling. The considered system comprises an external mass subjected to a symmetric three-dimensional linear local potential with an internal spherical rotator. The present study specifically focuses on the analysis of three-dimensional, dissipative mechanism of irreversible (unidirectional) energy transport across mutually orthogonal directions realized in the limit of low-energy excitations. In particular, this study unveils the special transient regimes of three-dimensional partial and complete transformation of in-plane vibrations of the external element to out-of-plane vibrations. Similar to the results reported in the first part of the series, this three-dimensional energy flow is fully governed by the motion of the internal spherical rotator coupled to the external mass. Analysis of this peculiar response regime is based on regular multi-scale asymptotic analysis resulting in a reduced order dissipative slow-flow model. Results of the analysis are substantiated by the numerical simulations of the full model.