Exploring the Possibility of Nonreciprocity via Geometric-Nonlinearity-Enabled All-Acoustic Spatiotemporal Modulation

Acoustic nonreciprocity has received significant interest, particularly in the context of enabling logic devices. One way to break reciprocity is through strategic spatiotemporal modulation of a material’s properties. In this work, we propose and analytically, computationally, and experimentally explore a concept composed of a quasi-one-dimensional nonlinear system, where the shear stiffness depends on longitudinal strain, with the aim that nonreciprocity of transverse–rotational waves could be enabled by the simultaneous propagation of a longitudinal wave injected from the boundary. Such an approach should require less computational overhead in contrast to systems wherein spatiotemporal modulation is accomplished by active control distributed throughout the material, and potentially enable scaling to smaller system sizes and higher frequencies. While good agreement, showing significant nonreciprocity, is found between our analytical predictions and our reduced-order, discrete element model (DEM) simulations, our higher fidelity, finite element model (FEM) simulations, and experiments do not show the same. We suggest that this qualitative difference is due to mechanical instability of the chain, which is not present in either DEM simulations or the analytical model. While providing a theoretical proposal for an all-acoustic spatiotemporally modulated nonreciprocal system, this work also identifies a critical limitation, namely, that of instability, which should be addressed in future related concepts.