The paper develops a new integral micromorphic elastic continuum model, which can describe dispersion properties of band-gap metamaterials, i.e., metamaterials that inhibit propagation of waves in a certain frequency range. The enrichment consists in nonlocal treatment of three terms in the expression for the potential energy density of the standard micromorphic continuum. After proper calibration, such a formulation can exactly reproduce two given branches of the dispersion curve (acoustic and optical), even in cases with a band gap. The calibration process exploits Fourier images of the unknown weight functions, which are analytically deduced from the dispersion relation of the material of interest. The weight functions are then reconstructed in the spatial domain by numerical evaluation of the inverse Fourier transform. The presented approach is validated on several examples, including discrete mass–spring chains with alternating masses, for which the dispersion relation has an explicit analytical form and the optical and acoustic branches are separated by a band gap.

中文翻译：

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在一维连续体中再现色散的积分微形态模型


本文开发了一种新的积分微晶弹性连续体模型，该模型可以描述带隙超材料的色散特性，即在一定频率范围内抑制波传播的超材料。富集包括对标准微晶连续体的势能密度表达式中的三个项进行非局部处理。经过适当的校准后，即使在带隙的情况下，这样的公式也可以精确地再现色散曲线的两个给定分支（声学和光学）。校准过程利用未知权重函数的傅里叶图像，这些图像是从目标材料的色散关系中分析推断出来的。然后通过逆傅里叶变换的数值计算在空间域中重建权重函数。所提出的方法在几个实例上得到了验证，包括具有交替质量的离散质量-弹簧链，其色散关系具有明确的解析形式，并且光学和声学分支由带隙分隔。