弹性-声学过渡中周期层状介质波传播的有效质量密度
Effective mass density for wave propagation in periodic layered media in the elasto-acoustic transition
AI总结：
本文结合传递矩阵法与Bloch定理解析周期层状介质的有效质量密度，首次阐明其从弹性各向同性到声学各向异性的过渡机制，揭示μ空间能带结构及例外点对过渡行为的关键影响。
AI中文摘要：
本文研究层状介质中声波与弹性波传播的有效质量密度，重点关注其在两种传播机制间的过渡特性。传统上，可通过无剪切极限从弹性力学控制方程推导出声学控制方程，但在考虑等效介质时，声学中通常得到的各向异性有效质量密度与弹性力学中的各向同性有效质量密度存在差异。此外，由于有效质量密度与剪切模量μ无关，对该极限的直接研究受到阻碍。为解决这一问题，本文将传递矩阵方法与Bloch定理相结合，推导了单胞由两层不同密度材料构成的周期材料的等效波数，再通过波数解析得到有效质量密度，从而可在两种传播机制下对其进行评估。此外，本文首次描述了周期层状介质中从各向同性弹性有效密度到各向异性声学有效密度的过渡过程。研究还证实了μ空间中能带结构的存在，以及例外点（exceptional points）的存在——在例外点处纵模与横模发生耦合，波变为倏逝波，这会显著影响弹性-声学过渡中有效密度的行为。
英文摘要：
This article investigates the effective mass density for acoustic and elastic wave propagation in layered media, with emphasis on its transition between these regimes. Conventionally, it is possible to recover the governing equations of acoustics from those of elasticity via the no-shear limit. However, when considering an effective medium, the anisotropic effective mass density typically obtained for acoustics differs from the isotropic one found in elasticity. Furthermore, direct investigation of this limit is hindered by the fact that the effective mass density is independent of the shear modulus $μ$. To tackle this problem, a transfer matrix approach is combined with Bloch's theorem to derive the effective wavenumber for a periodic material whose unit cell consists of two layers with different densities. The effective mass density is obtained analytically from the wavenumber, allowing for its evaluation in both regimes. Moreover, for the first time, a description of the transition from isotropic elastic to anisotropic acoustic effective density in a periodic layered medium is provided. Additionally, the existence of band structure in $μ$-space is demonstrated, along with exceptional points, where compressional and shear modes coalesce and waves become evanescent, which heavily affects the behaviour of the effective density in the elasto-acoustic transition.
