Locally Resonant Effective Phononic Crystals for Subwavelength Vibration Control of Torsional Cylindrical Waves
Locally Resonant Effective Phononic Crystals for Subwavelength Vibration Control of Torsional Cylindrical Waves
复制标题
用于扭转柱面波亚波长振动控制的局部谐振有效声子晶体
DOI：
10.1115/1.4052748
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Matlack, Kathryn H.
中科院分区：
文献类型：
--
作者：
Arretche, Ignacio;Matlack, Kathryn H.
局部共振材料允许在亚波长范围内控制波的传播。尽管这些材料不需要周期性，但它们通常被设计为周期性系统，因为这允许应用布洛赫定理和基于单个晶胞的整个系统的分析。然而，只有当我们假设平面波传播时，平移不变的几何形状才会导致具有周期系数的运动方程。当波前是圆柱形或球形时，通过单元格的镶嵌实现的系统不会导致周期系数，并且布洛赫定理不能应用。因此，大多数周期局部共振系统的研究仅限于平面波的传播。在这篇文章中，我们通过引入一个局部共振的有效声子晶体与附加扭转谐振器的径向变化的矩阵组成的解决这个限制。这种材料不是几何周期性的，但表现出有效的周期性，即，它的运动方程对于径向平移是不变的，这使得布洛赫定理可以应用于径向传播的扭转波。我们表明，这种材料可以在已经开发的超材料框架下进行分析。为了说明使用有效周期系统的重要性，我们将其行为与非有效周期但具有几何周期性的系统进行了比较。我们表现出相当大的差异，以及在这两个系统的负有效性能。局域共振有效声子晶体打开了在近场源的亚波长弹性波控制的可能性。
Locally resonant materials allow for wave propagation control in the subwavelength regime. Even though these materials do not need periodicity, they are usually designed as periodic systems since this allows for the application of the Bloch theorem and analysis of the entire system based on a single unit cell. However, geometries that are invariant to translation result in equations of motion with periodic coefficients only if we assume plane wave propagation. When wave fronts are cylindrical or spherical, a system realized through tessellation of a unit cell does not result in periodic coefficients and the Bloch theorem cannot be applied. Therefore, most studies of periodic locally resonant systems are limited to plane wave propagation. In this article, we address this limitation by introducing a locally resonant effective phononic crystal composed of a radially varying matrix with attached torsional resonators. This material is not geometrically periodic but exhibits effective periodicity, i.e., its equations of motion are invariant to radial translations, allowing the Bloch theorem to be applied to radially propagating torsional waves. We show that this material can be analyzed under the already developed framework for metamaterials. To show the importance of using an effectively periodic system, we compare its behavior to a system that is not effectively periodic but has geometric periodicity. We show considerable differences in transmission as well as in the negative effective properties of these two systems. Locally resonant effective phononic crystals open possibilities for subwavelength elastic wave control in the near field of sources.