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Evanescent waves in two-dimensional fluid-saturated porous metamaterials with a transversely isotropic matrix

机译：具有横向各向同性基质的二维流体饱和多孔超材料的渐逝波

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摘要

Wave propagation in a two-dimensional periodic fluid-saturated porous metamaterial (FSPM) is investigated. The constitutive relation considered for fluid-saturated porous materials is based on Biot's homogeneization theory. Such media generally support two shear and two longitudinal elastic waves. Anisotropic wave propagation results both from anisotropy of the solid matrix and from the periodic structure of the metamaterial. Special attention is devoted to the dispersion and attenuation of evanescent Bloch waves in a FSPM whose matrix is transversely isotropic in which case in-plane elastic waves are a superposition of one shear wave and of two longitudinal waves. Bloch waves, complex band structures, and transmission properties are obtained numerically using finite element analysis. The case of homogeneous fluid-saturated porous media is considered since numerical simulations can be compared directly with analytic results in this case. The effects of material anisotropy and of fluid viscosity on wave propagation in two-dimensional FSPM are then discussed. It is found that wave-number band gaps appear in the complex band structure of the lossless FSPM due to the interference of waves with different but nonorthogonal polarizations. Wave-number band gaps are connected continuously by complex-frequency bands, hence, defining stop bands in the time domain. No complete frequency band gaps are found in two-dimensional lossless FSPM. in contrast to the one-dimensional case [Y.-F. Wang et al. Phys. Rev. B 99, 134304 (2019)] due to the presence of the additional quasishear wave accompanying the two quasilongitudinal waves. Both the complex band structure and the transmission properties are affected by the anisotropy of the solid matrix. Wide transmission dips come up when viscosity is introduced as a result of the strong attenuation and the coupling of all wave polarizations. Concurrently, wave-number band gaps are washed out by viscosity. This theoretical paper has relevance to practical applications of fluid-saturated porous metamaterials. e.g., in concrete structures and geological soils.
机译：研究了二维周期性流体饱和多孔超材料（FSPM）中的波传播。考虑流体饱和多孔材料的本构关系是基于Biot的均匀化理论。这种介质通常支持两个剪切和两个纵向弹性波。各向异性波传播从固体矩阵的各向异性和超材料的周期性结构产生。特别注意在横向各向同性的FSPM中致散和衰减，其基质被横向各向同性，在这种情况下，面内弹性波是一个剪切波和两个纵向波的叠加。使用有限元分析，在数值上进行数字地获得Bloch波，复杂带结构和传动特性。考虑了均匀流体饱和多孔介质的情况，因为在这种情况下可以直接与分析结果直接比较数值模拟。然后讨论了材料各向异性和流体粘度对二维FSPM的波传播的影响。发现由于波浪与不同但非正交偏振的波浪的干扰，波数带隙出现在无损FSPM的复杂带结构中。波浪数带间隙由复频带连续连接，因此，在时域中定义停止频带。在二维无损FSPM中没有找到完整的频带间隙。与一维案例相比，[Y.-f. Wang等人。物理。 Rev.B 99,134304（2019）]由于存在伴随两波的附加Quasishear波。复杂频带结构和传输属性都受到固体矩阵的各向异性的影响。由于强的衰减和所有波偏振的耦合而引入粘度，宽传输蘸倍。同时，波浪数带间隙通过粘度洗掉。该理论纸具有与流体饱和多孔超材料的实际应用有关。例如，在混凝土结构和地质土壤中。

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  • 来源
    《Physical review》 |2020年第18期|184301.1-184301.13|共13页
  • 作者

    Yan-Feng Wang; Jun-Wei Liang; A-Li Chen; Yue-Sheng Wang; Vincent Laude;

  • 作者单位

    Department of Mechanics School of Mechanical Engineering Tianjin University 300350 Tianjin China;

    Institute of Engineering Mechanics Beijing Jiaotong University 100044 Beijing China China Railway Construction Investment Group Corporation Limited 100044 Beijing China;

    Institute of Engineering Mechanics Beijing Jiaotong University 100044 Beijing China;

    Department of Mechanics School of Mechanical Engineering Tianjin University 300350 Tianjin China;

    Institut FEMTO-ST Universite Bourgogne Franche-Comte CNRS 25030 Besancon France;

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