Regimes of two-dimensional energy channeling in the inertially coupled unit-cell model subjected to an asymmetric potential

We analyze the stationary and non-stationary states emerging in a two-dimensional (2D) model consisting of an outer element that incorporates an internal rotator and is subjected to a 2D anharmonic and non-symmetric local potential. We focus on the effect of the asymmetry of the potential on the mechanism of formation and bifurcations of various stationary and non-stationary regimes in the system. The non-stationary regimes are characterized by an intense bi-directional energy transfer between the axial and lateral vibrations of the main element as well as the regimes of unidirectional energy locking. We show that the transitions between the different states of the system are controlled by the motion of the internal rotator. Our analysis is based on the complexification-averaging procedure and the singular multiscale asymptotic method. Investigation of the system's dynamics in the vicinity of the 1:1:1 resonance enables us to reproduce the bifurcation structure of the stationary regimes and describe the formation mechanisms of highly non-stationary states of intense energy transfer. Our analysis shows that the most important effect of the asymmetric potential is the breakdown of a unique complete bi-directional energy channeling mechanism into two separate mechanisms that correspond to incomplete horizontal-to-vertical and vertical-to-horizontal energy transfer, respectively, and are enabled at two different critical values of the main bifurcation parameter. Results of the analysis are in good agreement with the numerical simulations of the full model. (C) 2019 Published by Elsevier Ltd.