Abstract
We numerically investigate the supratransmission phenomenon in an active nonlinear system modeled by the 1D/2D discrete sine-Gordon equation with non-local feedback. While, at a given frequency, the typical passive system exhibits a single amplitude threshold marking the onset of the phenomenon, we show that the inclusion of non-local feedback manifests additional thresholds that depend upon the specific boundary from which supratransmission is stimulated, realizing asymmetric (i.e., non-reciprocal) dynamics. The results illustrate a new means of controlling nonlinear wave propagation and energy transport for, e.g., signal amplification and mechanical logic.
Highlights
We present an approach to asymmetric wave propagation in nonlinear mechanical networks with a focus on energy transmission within the band gap
We numerically investigate the dynamics of a representative nonlinear network with non-local feedback
We numerically investigated the nonlinear supratransmission phenomenon in active 1D/2D periodic networks characterized by a non-local feedback control
Summary
Regarding phononic materials [3,21,22,23,24], inherent nonreciprocity has been demonstrated in a number of systems utilizing unique and intersecting strategies for microstructure design, i.e., internal architectures characterized by internal motion [25,26], time-dependent [27,28,29] and topological [30,31,32] properties, and nonlinearity [33,34,35] The focus of these and parallel studies is linear wave manipulation. Unique in the supratransmission literature, these lattice materials incorporate active elements which impart a local, non-conservative forcing proportional to non-local degrees-of-freedom The result of this construction is that the onset of the supratransmission phenomenon is a function of the driving parameters (i.e., frequency and amplitude) but the specific network boundary at which the excitation is applied and from which wave energy is transmitted to the medium, establishing the asymmetric dynamic behavior.
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