Pham Kim, Maurel Agnès, Félix Simon, Guenneau Sébastien
IMSIA, ENSTA ParisTech, 828 Bd des Maréchaux, 91732 Palaiseau, France.
Institut Langevin, CNRS, ESPCI ParisTech, 1 rue Jussieu, 75005 Paris, France.
Materials (Basel). 2020 Apr 1;13(7):1632. doi: 10.3390/ma13071632.
This study follows from Maurel et al., Phys. Rev. B 98, 134311 (2018), where we reported on direct numerical observations of out-of-plane shear surface waves propagating along an array of plates atop a guiding layer, as a model for a forest of trees. We derived closed form dispersion relations using the homogenization procedure and investigated the effect of heterogeneities at the top of the plates (the foliage of trees). Here, we extend the study to the derivation of a homogenized model accounting for heterogeneities at both endings of the plates. The derivation is presented in the time domain, which allows for an energetic analysis of the effective problem. The effect of these heterogeneous endings on the properties of the surface waves is inspected for hard heterogeneities. It is shown that top heterogeneities affect the resonances of the plates, hence modifying the cut-off frequencies of a wave mathematically similar to the so-called Spoof Plasmon Polariton (SPP) wave, while the bottom heterogeneities affect the behavior of the layer, hence modifying the dispersion relation of the Love waves. The complete system simply mixes these two ingredients, resulting in hybrid surface waves accurately described by our model.
本研究延续了莫雷尔等人发表于《物理评论B》第98卷，第134311页（2018年）的工作，在该研究中我们报道了沿位于引导层之上的一排平板传播的面外剪切表面波的直接数值观测结果，将其作为树木森林的一个模型。我们使用均匀化方法推导了封闭形式的色散关系，并研究了平板顶部（树叶）的不均匀性的影响。在此，我们将研究扩展到推导一个考虑平板两端不均匀性的均匀化模型。推导过程在时域中给出，这使得我们能够对有效问题进行能量分析。针对硬不均匀性情况，研究了这些不均匀的端部对表面波特性的影响。结果表明，顶部不均匀性影响平板的共振，从而在数学上改变了一种与所谓的仿表面等离激元极化激元（SPP）波类似的波的截止频率，而底部不均匀性影响层的行为，从而改变了乐甫波的色散关系。整个系统简单地混合了这两种因素，产生了我们的模型能够精确描述的混合表面波。
