半无限柏拉图晶体中弯曲波的控制
Controlling flexural waves in semi-infinite platonic crystals
摘要：
我们解决的问题，通过一个半无限阵列的点散射体/谐振器，它采取各种物理上有趣的形式的平面弯曲波的散射和传输。数学模型考虑了几类点缺陷，包括质量弹簧谐振器连接到弯曲板的上表面和集中点质量的限制情况。我们还分析了特殊情况下的谐振器连接到板的相对面。这个问题被减少到一个功能方程的维纳-霍普夫型，其内核的散射体的类型而异。一种新的方法，它源于半无限系统的核函数和相应的无限系统的准周期格林函数之间的直接联系，用于识别特殊的频率制度。因此，我们展示了动态各向异性波效应在半无限柏拉图晶体，特别注意设计系统，表现出动态中性（完美的传输）和本地化接近结构化界面。
英文摘要：
We address the problem of scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener-Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems to exhibit dynamic neutrality (perfect transmission) and localisation close to the structured interface.
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