Abstract The star-shaped lattice structure is recognized as a typical auxetic metamaterial. Unlike the most research focused on the negative Poisson's ratio, in this paper the wave propagation behaviour and vibration attenuation mechanism of the periodic star-shaped lattice structure are studied based on the analytical 16 degrees of freedom (DOF) discrete mass-spring model. The dispersion relation and bandgaps of the 16 DOF mass-spring model are derived based on lattice dynamics. The dependence of the bandgap boundaries on the parameters of configuration angle, stiffness, and mass are studied accordingly. It is noteworthy that the eigenstate modes investigation reveals that the bandgaps attribute to the hybridization of the monopole, dipole, quadrupole, and rotational resonance, which is only noticed in multiphase hybrid metamaterials before. Most importantly, though examining the eigenstate modes of the degeneration points, the low-frequency bandgap between the acoustic and optical dispersion curves is opened by tuning the dominant parameters. The response of the finite periodic star-shaped lattice shows the frequency ranges with high attenuation agree well with complete bandgaps predicted by dispersion relation. The star-shaped lattice shows a very unique anisotropic solid when the slope of the dispersion curve is negative.

中文翻译：

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星形晶格结构的多极共振与带隙形成机制

摘要 星形晶格结构被认为是一种典型的拉胀超材料。与大多数研究集中在负泊松比不同，本文基于解析的 16 自由度 (DOF) 离散质量弹簧模型研究了周期性星形晶格结构的波传播行为和振动衰减机制。16自由度质量-弹簧模型的色散关系和带隙是基于晶格动力学推导出来的。相应地研究了带隙边界对配置角、刚度和质量参数的依赖性。值得注意的是，本征态模式研究表明，带隙归因于单极子、偶极子、四极子和旋转共振的杂化，这在以前只在多相杂化超材料中被注意到。最重要的是，通过检查退化点的本征态模式，通过调整主要参数打开了声学和光学色散曲线之间的低频带隙。有限周期星形晶格的响应表明高衰减的频率范围与色散关系预测的完整带隙非常吻合。当色散曲线的斜率为负时，星形晶格显示出非常独特的各向异性固体。有限周期星形晶格的响应表明高衰减的频率范围与色散关系预测的完整带隙非常吻合。当色散曲线的斜率为负时，星形晶格显示出非常独特的各向异性固体。有限周期星形晶格的响应表明高衰减的频率范围与色散关系预测的完整带隙非常吻合。当色散曲线的斜率为负时，星形晶格显示出非常独特的各向异性固体。