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We investigate wave propagation in in-plane rotator lattices and demonstrate dispersion morphing and extreme acoustoelastic effects using analytical and numerical means. By changing the angle of the rotator arms attaching the elastic linkage between adjacent rotators, we show that the band structure may morph from a positive/negative-group-velocity passband into a flat band across the whole wavenumber space, and then into a negative/positive-group-velocity passband. A similar process can also occur at certain fixed arm angles when the lattice constant changes, which one may interpret as stretching or compressing the structure along the lattice directions, effectively mimicking the acoustoelastic effect. We analytically investigate both processes and provide closed-form expressions for the occurrence of flat bands, which indicates the transition of the passband property. Further, we explore a chiral rotator lattice design where the oscillation equilibrium position for each rotator may shift upon the change of the lattice constant. This design has a unique advantage that the morphed passband maintains approximately the same frequency range such that a signal may stay propagating during the process of dispersion morphing. In the end, we present numerical simulations for three potential applications utilizing the aforementioned findings. In these applications, both static and dynamic lattice stretching are considered, resulting in on-demand bi-directional wave-guiding, refraction bending, and time-modulated amplifying. Numerical simulations document a high-quality agreement with theory and yield promising results that may inspire next-generation reconfigurable metamaterials. 

Abstract Acoustic non-reciprocity, referring to the phenomenon of path-dependent propagation, has diverse applications in mechanical devices. This paper presents a numerical study on a periodic triangle-shape structure that breaks reciprocity in a passive manner over a broad range of frequency and energy. The proposed structure contains strong nonlinearity and geometric asymmetry, which contributes to a direction-dependent dispersion relationship. When the signal frequency falls in the band pass in one direction, and band gap in the other, a unidirectional wave propagation results. The system achieves giant non-reciprocity with minimal distortion in the frequency content of the signal. 

Acoustic reciprocity, which is widely observed in linear time-invariant systems, refers to the property that wave transmission pattern remains the same when the source and receiver are switched. Non-reciprocity, on the other hand, violates this symmetry and can be used to control wave propagation and manufacture desired propagation patterns. To break reciprocity, multiple approaches (active and passive) have been studied recently. While active manner often relies on odd-symmetry field or time-variant parameters, passive manner achieves non-reciprocity by combining geometric asymmetry and nonlinearity in the structure. In this field, researchers have studied a number of acoustic devices that allow one-way propagation1, 2. However, these devices either change the frequency content of the sending signal, or have a strict restriction on the range of sending frequency. In this paper, we propose a passive, nonlinear, periodic structure, which achieves giant non-reciprocity for a range of input frequency and energy with minimal distortion of the sending frequency.