标题： 二维高对比弹性介质中的亚波长共振 显示英文标题

标题： Subwavelength resonances in two-dimensional elastic media with high contrast

摘要： 本文采用层势技术研究二维弹性介质中波的散射，该介质在Lamé参数和密度方面具有高对比度。 我们的贡献有四点。 首先，我们基于边界积分算子的核空间构造了一个可逆算子，这使得可以通过正交条件表征共振频率。 其次，我们使用渐近分析推导出这些共振频率主导项的 governing 方程。 第三，我们分析了不同频段入射频率下内部区域的散射场，并表征了外部区域的纵向和横向远场模式。 最后，我们研究了稀疏结构声子晶体中的亚波长带隙。 显示英文摘要

摘要： This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lam\'{e} parameters and density. Our contributions are fourfold. First, we construct an invertible operator based on the kernel spaces of boundary integral operators, which enables the characterization of resonant frequencies through an orthogonality condition. Second, we use asymptotic analysis to derive the equation governing the leading-order terms of these resonant frequencies. Third, we analyze the scattered field in the interior domain for incident frequencies across different regimes and characterize the longitudinal and transverse far-field patterns in the exterior domain. Finally, we examine the subwavelength bandgap in the phononic crystal with a dilute structure.