Tunable Acoustic Nonreciprocity in Strongly Nonlinear Waveguides with Asymmetry

In linear acoustics, the reciprocal behavior of waves traveling in periodic materials can be manipulated by imposing external or configurational biases to the system. However, the nonreciprocity observed in linear systems is energetically expensive. We demonstrate that strongly nonlinear, asymmetric lattices can be designed to exhibit strong nonreciprocity that is passively adaptive and tunable. An alternative class of waveguides consisting of two coupled nonlinear lattices, one stiffer than the other, allows wave propagation preferentially in one direction at certain energy ranges. This "giant" nonreciprocal behavior is obtained passively by tuning the propagation zones of these lattices in the frequency-energy domain. We present numerical simulations corroborated by experiments to show an instance of this alternative class of nonlinear waveguides. Specifically, at low input energy, wave packets generated by an applied impulse at the lateral boundaries of the waveguide are blocked at the interface of the two lattices. However, at intermediate energy ranges, wave packets initiated at the free boundary of the softer lattice propagate through the waveguide, whereas wave packets initiated at the free boundary of the stiffer lattice are blocked at the interface. The nonreciprocal acoustics persist until at the critical level of input energy, above which waves propagate in both directions within the waveguide. The range of energy over which nonreciprocal wave transmission occurs is passively tunable by appropriately manipulating the nonlinear propagation zones of the lattices in the frequency-energy domain. The nonreciprocity concept is applicable to materials and systems capable of exhibiting strongly nonlinear behavior and can find broad applications in cases where passive targeted (directed) energy transfer in space and/or frequency is a desired outcome. For example, nonlinear nonreciprocal metamaterials can be used in passive acoustic isolation designs with the capacity for unidirectional sound transmission, thus eliminating their "acoustic signature"; in ultrasonics, to yield better wave focusing at preferential frequencies, and thus improved signal-to-noise ratios; in shock isolation systems, for example, by rapid nonreciprocal low-to-high nonlinear energy transfers, yielding fast structural response attenuation; or in networks of coupled oscillators enabling passive, irreversible energy transmission in preferential directions. Clearly, such capabilities for passive nonreciprocity are not attainable in linear systems.