Philos Trans A Math Phys Eng Sci
August 2018
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.
View Article and Find Full Text PDFPresent 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.
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