Nonlinear energy channeling in the two-dimensional, locally resonant, unit-cell model. II. Low energy excitations and unidirectional energy transport.

This paper completes a series of two publications devoted to the analytical investigation of energy channeling phenomena, emerging in a locally resonant unit-cell model. The system under consideration comprises an outer mass with internal rotator and subject to the 2D nonlinear local potential. In the present study, we focus on the analysis of the regimes of two-dimensional, nonlinear energy transport forming in the special asymptotic limit of low energy excitations. Unlike the previously considered case, this limit can also be characterized by the absence of resonant interactions between the internal rotator and the motion of an outer element. In the considered limit, we report the emergence of all new, highly nonlinear, transient regimes of unidirectional energy channeling. This phenomenon is manifested by partial and complete targeted energy flow from axial to lateral vibrations, controlled by an internal device. Here, we also show that regimes corresponding to the bidirectional energy channeling as well as the spontaneous energy locking reported in the first paper of the series-persist in the low energy limit as well. In this study, we use a regular multi-scale asymptotic procedure and completely unveil the intrinsic mechanisms governing bi- and unidirectional energy channeling. Numerical simulations are found to be in a fairly good agreement with the predictions of analytic model.