This paper aims to enhance and tune wave-propagation characteristics of periodic architected structures by adding auxiliary resonators made of functionally graded materials (FGMs). For this purpose, cantilever FGM beams are added to periodic metamaterials with square and hexagonal topologies, and the effects of the material distribution of the added resonators on their wave-attenuation performance are analyzed. More specifically, a combination of locally resonant and Bragg-type bandgaps is formed as a result of adding FGM resonators, while the conventional structures have no bandgap in the considered region. The studied low-frequency region is of high importance, and the appearance of wide bandgaps there opens horizons for new structural and acoustic applications. Further, these bandgaps depend on the material parameters of the resonators, and their location and width are changed, systematically as functions of the elastic modulus ratio, density ratio, and non-negative power-law exponent of the resonators. For the numerical analysis, a finite element formulation is developed for an FGM beam, and the wave propagation is studied using Bloch’s theorem. According to the results, with increasing the elastic modulus contrast of the auxiliary FGM resonators, the locations of the bandgaps move higher, while increasing the density ratio contrast moves them to lower frequencies. Additionally, the effect of adding auxiliary FGM resonators on the directionality of the wave propagation is studied using the iso-frequency contours of the first dispersion branches of each structure. The results of the present study can be a starting point for using FGM resonators to design tunable elastic/acoustic metamaterials with the ability to filter waves in predefined frequency ranges.

中文翻译：

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具有由功能梯度材料制成的辅助谐振器的混合晶格超材料

本文旨在通过添加由功能梯度材料 (FGM) 制成的辅助谐振器来增强和调整周期性建筑结构的波传播特性。为此，将悬臂 FGM 梁添加到具有方形和六边形拓扑结构的周期性超材料中，并分析了添加的谐振器的材料分布对其波衰减性能的影响。更具体地说，由于添加了 FGM 谐振器，形成了局部谐振和布拉格型带隙的组合，而传统结构在所考虑的区域中没有带隙。所研究的低频区域非常重要，宽带隙的出现为新的结构和声学应用打开了视野。此外，这些带隙取决于谐振器的材料参数，并且它们的位置和宽度被系统地改变，作为谐振器的弹性模量比、密度比和非负幂律指数的函数。对于数值分析，为 FGM 梁开发了有限元公式，并使用布洛赫定理研究了波的传播。根据结果​​，随着辅助 FGM 谐振器的弹性模量对比度的增加，带隙的位置移动得更高，而密度比对比度的增加将它们移动到更低的频率。此外，使用每个结构的第一色散分支的等频轮廓来研究添加辅助 FGM 谐振器对波传播方向性的影响。