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Pulse transmission and acoustic non-reciprocity in a granular channel with symmetry-breaking clearances

机译：具有对称破坏间隙的颗粒状通道中的脉冲传输和声学非可逆性

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Granular media composed of ordered arrays of discrete spherical granules have attracted considerable attention due to their highly nonlinear and discontinuous dynamics and acoustics that enable passively adaptive and tailorable properties. In this work we numerically study nonlinear pulse propagation in a two-dimensional (2D) granular channel composed of a main homogeneous lattice with several pairs of side granules. Depending on the direction of pulse transmission in the main lattice, a periodic series of symmetry-breaking clearances alter the topology of this 2D granular network. The rotational dynamics of the individual granules, as well as dissipative effects due to friction between granules (and their boundaries) and inherent material damping, are proven to play a significant role in the acoustics of the granular channel. This is demonstrated by comparing the theoretical predictions of this work to experimental measurements of the same system reported earlier. Moreover, the strong nonlinearity of this system in synergy with the topological asymmetry introduced by the clearances passively breaks acoustic reciprocity. To this end, a detailed study of pulse transmission in the 2D granular channel is performed, and it is shown that by simply changing the direction of pulse transmission it is possible to switch the nonlinear acoustics from Nesterenko solitary pulses to strongly decaying propagating pulses. In the latter case there is continuous and irreversible transfer of energy from the main propagating pulse to the side granules, which act, in essence, as nonlinear energy absorbers. This work highlights the important role that (even small) geometric imperfections (asymmetries) may play on the acoustics of 2D granular media.
机译：由离散球形颗粒的有序阵列组成的颗粒介质由于具有高度的非线性和不连续的动力学和声学特性而吸引了相当大的关注，它们具有被动适应性和可定制性。在这项工作中，我们对二维（2D）颗粒通道中的非线性脉冲传播进行了数值研究，该通道由主要的均匀晶格和几对侧颗粒组成。根据主晶格中脉冲传输的方向，周期性的一系列对称破坏间隙会更改此2D粒度网络的拓扑。事实证明，单个颗粒的旋转动力学以及颗粒之间的摩擦（及其边界）和固有的材料阻尼引起的耗散效应在颗粒通道的声学中起着重要作用。通过将这项工作的理论预测与先前报道的同一系统的实验测量值进行比较，可以证明这一点。此外，与间隙引起的拓扑不对称性协同作用的该系统的强非线性特性被动地破坏了声学互易性。为此，对二维颗粒通道中的脉冲传输进行了详细的研究，结果表明，仅通过改变脉冲传输的方向，就可以将非线性声学从Nesterenko孤立脉冲转换为强烈衰减的传播脉冲。在后一种情况下，能量从主传播脉冲连续且不可逆地转移到侧部颗粒，这些颗粒本质上起非线性能量吸收器的作用。这项工作强调了（甚至很小的）几何缺陷（不对称性）可能在2D颗粒介质的声学中发挥的重要作用。

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