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Elastic wave propagation in triangular chiral lattices: Geometric frustration behavior of standing wave modes

机译：三角手性格子中的弹性波传播：常设波模式的几何挫折行为

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The paper presents an investigation of elastic wave propagation in triangular chiral lattices composed of zigzag beams. Considerable attention is focused on the formation of band gaps, where a wave with specific frequency is forbidden from passing through the material. Band structure analysis reveals that compared with the conventional triangular configuration with straight cell walls, the emerging band gaps are characterized by their upper bounding modes performing rotational deformation shapes. Owing to the geometric constraint of the triangle topology, the symmetric rotation standing mode, which is present in the band gap edges of both hexagonal and square chiral honeycombs, is frustrated into a complex deformation pattern, leading to a higher band-gap edge frequency for the triangular chiral lattices. Meanwhile, the natural frequency of the simple heuristic model, a cell wall with two ends simply supported, also fails to predict the bounding frequency corresponding to the frustrated standing mode. A modified heuristic model is constructed according to the free vibration analysis of a triangular frame, which provides a rotation relationship with regard to the three junctions, i.e., the sum of the rotational angles is zero. The natural frequency of the modified heuristic model provides an accurate estimation of the band frequency of the geometrically frustrated standing mode. Our findings illustrate the geometric frustration phenomenon with respect to elastic wave propagation in triangular periodic lattices, which is beneficial for the band gap width enhancement, thus facilitating vibration suppression. (C) 2018 Published by Elsevier Ltd.
机译：本文介绍了由锯齿形梁组成的三角手性格子中弹性波传播的研究。相当大的关注集中在带间隙的形成上，其中禁止具有特定频率的波浪通过材料。频带结构分析显示，与具有直电池壁的传统三角形结构相比，新出现带间隙的特征在于它们的上限制模式执行旋转变形形状。由于三角形拓扑的几何约束，存在于六边形和方形手性蜂窝状的带隙边缘中的对称旋转立式模式被挫折成复杂的变形图案，导致更高的带间隙边缘频率三角形手性格子。同时，简单启发式模型的自然频率，一种具有两个端部的细胞壁，简单地支持，也不能预测对应于沮丧的站立模式的边界频率。根据三角形框架的自由振动分析构造改进的启发式模型，其提供了关于三个结的旋转关系，即旋转角度为零。改进的启发式模型的自然频率提供了几何挫败站立模式的频带频率的精确估计。我们的研究结果说明了三角形周期晶格中的弹性波传播的几何挫折现象，这对于带隙宽度增强有益，从而便于振动抑制。 （c）2018由elestvier有限公司出版

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