Physical realization and experimental validation of effective phononic crystals for control of radial torsional waves
Physical realization and experimental validation of effective phononic crystals for control of radial torsional waves
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DOI：
10.1016/j.jsv.2022.117305
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发表时间：
2022-09-19
影响因子：
4.7
通讯作者：
Matlack, Kathryn H.
中科院分区：
文献类型：
--
作者：
Arretche, Ignacio;Matlack, Kathryn H.
最近，有效声子晶体（EPC）和局部共振有效光子晶体（LREPC）的概念已经被提出，以使声子晶体（PC）和声学超材料（AM）的属性，分别在径向传播波。这个问题并不简单，因为径向周期系统的运动方程没有周期系数，因此这些径向周期系统中的布洛赫解是无效的。为了克服这一点，EPC和LREPC使用径向相关的属性来强制径向弹性波运动方程中的周期系数，从而使布洛赫定理的应用成为可能，从而允许PC和AM的属性。然而，所需的径向相关性质使其物理实现严重复杂化，因为必须调整模量和密度，使其遵循特定的径向变化。在本文中，我们提出了一种方法来实现物理LREPC通过径向变化其阻抗通过空间变化到其面外厚度。LREPC的物理实现也涉及局部扭转共振。与典型的AM相比，LREPC中的谐振器必须在几何形状上不同，以在不同半径处保持相同的扭转刚度和惯性矩。我们使用增材制造加上传统机械加工来制造LREPC。我们介绍了一个实验装置，以测量径向传播的扭转波在LRPEC和如何解耦扭转振动从弯曲振动，以准确地测量传输。为了显示使用LREPC的重要性，我们比较其动态响应的局部共振均匀系统（LRHS），一个系统，是径向周期性的，但具有非周期性的运动方程。测量的透射率表明，只有LREPC衰减的带隙频率内的波由布洛赫分析预测。这项工作的实验表明，LREPC允许应用众所周知的概念AM控制径向传播的扭转波。
Recently, the concept of effective phononic crystals (EPCs) and locally resonant effective pho-nonic crystals (LREPCs) have been proposed to enable properties of phononic crystals (PCs) and acoustic metamaterials (AMs), respectively, in radially propagating waves. This problem is not straightforward since the equations of motion of radially periodic systems do not have periodic coefficients and thus Bloch solutions in these radially periodic systems are not valid. To overcome this, EPCs and LREPCs use radially dependent properties to force periodic coefficients in the equations of motion of radial elastic waves, enabling the application of the Bloch theorem and thus allowing for properties of PCs and AMs. However, the required radially dependent properties severely complicate their physical realization, since modulus and density must be tailored such that they follow a specific radial variation. In this paper, we propose a method to physically realize an LREPC by radially varying its impedance through spatial changes to its out-of-plane thickness. Physical realization of the LREPC also involves local torsional resonances. In contrast to typical AMs, the resonators in the LREPC must be geometrically different to retain the same torsional stiffness and moment of inertia at different radii. We use additive manufacturing plus traditional machining to fabricate the LREPC. We introduce an experimental setup to mea-sure radially propagating torsional waves in the LRPEC and show how to decouple torsional vi-brations from bending vibrations to accurately measure transmission. To show the importance of using an LREPC, we compare its dynamic response to a locally resonant homogenous system (LRHS), a system that is radially periodic but has non-periodic equations of motion. Measured transmission shows that only the LREPC attenuates waves inside the band gap frequencies pre-dicted by Bloch analysis. This work experimentally shows that LREPCs allow for the application of well-known concepts of AMs to control radially propagating torsional waves.