For linear, small-amplitude waves,&nbsp;phononic crystals and acoustic metamaterials&nbsp;regulate&nbsp;internal scattering and resonance phenomena such that the Fourier components of a disturbance penetrate the material within only particular frequency ranges and in all or specific directions; outside these pass bands, i.e., within the band gaps, wave propagation is prohibited&nbsp;and the associated wave energy decays exponentially in space. Nevertheless, non-linearities inherent to the microstructure enable a unique dynamic response for large amplitude waves. Supratransmission describes the spontaneous flow of energy within the band gap via the non-linear (non-topological) modes of a medium activated by a boundary driving of sufficient amplitude. This may be exploited, e.g., for the transmission of binary, non-linear signals in lightly-damped systems, as well as for the digital amplification of exceptionally weak signals for sensing.&nbsp;Functionality of such devices is expanded by the introduction of directional response.&nbsp;Reciprocity describes the symmetry of wave transmission between two points in space: if a source and receiver exchange positions, the corresponding frequency&nbsp;response function is identical even in the presence of inhomogeneities and losses.&nbsp;Regarding phononic materials,&nbsp;inherent non-reciprocity has been demonstrated in a number of systems utilizing unique and intersecting strategies for microstructure design, i.e., internal architectures characterized by internal motion, time-dependent&nbsp;and topological&nbsp;properties, and non-linearity. The focus of these and parallel studies is linear wave manipulation. Transition waves – non-linear (topological) modes characteristic of multi-stable systems which propagate by liberating stored elastic energy – demonstrate non-reciprocity as well; however, they are energetically limited to one-time operation or short propagation distances. In the context of supratransmission,&nbsp;spatial asymmetry in the metamaterial construction has been usedto elicit non-reciprocal transmission.&nbsp;&nbsp;While most of the previous references employ a passive material platform, a small but growing collection investigate linear wave propagation within in an active setting. Recently, feedback control integrated directly into the material architecture has opened the door to more complex interactions unavailable in traditional structures and have been shown to be capable of eliciting non-reciprocal behavior. Uniquely, rather than injecting energy into (or extracting from) the system by an external means, feedback involves observing the state of the system and then, following predetermined relations, generating a response that alters the present state. As a result the material behavior is inherent rather than a function of environmental conditions (e.g., temperature, external fields, pumps, actuators which behave independently of the system).&nbsp;At present, the supratransmission phenomenon in feedback mediated non-linear networks has yet to be investigatedWe numerically investigate the supratransmission phenomenon in an active non-linear 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 non-reciprocal dynamics. The results illustrate a new means of controlling non-linear wave propagation and energy transport for, e.g., signal amplification and mechanical logic.

Enabling Asymmetric Supratransmission in  Mechanical Lattices Through Active Non-Local Feedback Control

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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