Dispersion and topological characteristics of permutative polyatomic phononic crystals
Dispersion and topological characteristics of permutative polyatomic phononic crystals
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DOI：
10.1098/rspa.2019.0022
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发表时间：
2019-06
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影响因子：
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通讯作者：
H. A. Ba'ba'a;Mostafa Nouh;Tarunraj Singh
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文献类型：
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作者：
H. A. Ba'ba'a;Mostafa Nouh;Tarunraj Singh
本文提出了一种对声子晶体（PC）的综合数学处理方法，它包括一个由重复的多原子晶胞组成的有限晶格。波在多原子晶格中的色散容易受到构成单个晶胞的单原子（子晶胞）的局部排列的变化的影响。我们推导和解释的条件，导致相同的和对比的频带结构，以及作为循环和非循环细胞排列的结果，不同的本征模的可能性。与循环排列相关联的不同模式产生拓扑不变性，其通过复本征模的缠绕数来评估。波拓扑变化的多原子PC的量化和所需的条件，以支持边缘模式在这样的晶格建立。接下来，有限多原子PC的传递函数分析被用来解释多个布拉格带隙的形成以及截断共振的出现。进一步利用无限晶格截断产生的异常来设计扩展晶格中的镜像对称边缘模式。我们的结论与一个广义的解释的基础上的Bode图分析的带隙演化机制。
This work presents a comprehensive mathematical treatment of phononic crystals (PCs) which comprise a finite lattice of repeated polyatomic unit cells. Wave dispersion in polyatomic lattices is susceptible to changes in the local arrangement of the monatoms (subcells) constituting the individual unit cell. We derive and interpret conditions leading to identical and contrasting band structures as well as the possibility of distinct eigenmodes as a result of cyclic and non-cyclic cellular permutations. Different modes associated with cyclic permutations yield topological invariance, which is assessed via the winding number of the complex eigenmode. Wave topology variations in the polyatomic PCs are quantified and conditions required to support edge modes in such lattices are established. Next, a transfer function analysis of finite polyatomic PCs is used to explain the formation of multiple Bragg band gaps as well as the emergence of truncation resonances within them. Anomalies arising from the truncation of the infinite lattice are further exploited to design mirror symmetrical edge modes in an extended lattice. We conclude with a generalized explanation of the band gap evolution mechanism based on the Bode plot analysis.