Acoustic metamaterials for sound focusing and confinement
Acoustic metamaterials for sound focusing and confinement
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DOI：
10.1088/1367-2630/9/11/399
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发表时间：
2007-11-06
影响因子：
3.3
通讯作者：
Ramakrishna, S. Anantha
中科院分区：
文献类型：
--
作者：
Guenneau, Sebastien;Movchan, Alexander;Ramakrishna, S. Anantha
我们给出了一个理论设计的局部共振二维圆柱结构，涉及一对C形的空隙在弹性介质中，我们称之为双“C”谐振器（DCR）和嵌入薄刚性杆，显示负折射效应在低频区。DCR负责低频带隙，该低频带隙与细条的存在相关联的微小间隙混合。使用渐近分析，典型的工作频率给出了封闭的形式：DCR表现为亥姆霍兹共振器建模的质量连接到夹紧的墙壁上的弹簧在任何一侧，而细酒吧表现为一个周期性的双原子链的质量连接弹簧。离散模型给出了一个精确的描述的位置和宽度的阻带的情况下的DCR和前两个色散带的周期性细杆。然后，我们结合联合收割机我们的渐近公式的阵列的DCR和薄杆设计的复合结构，显示负折射效应，并具有负相速度在一个频带内，从而表现在许多方面作为一个负折射声介质（NRAM）。有限元计算表明，在这个频率下，这样的NRAM的板作为声子平面超透镜工作，而这样的NRAM的共享顶点的两个角作为开放的谐振器，并且可以用于将声音限制在一定程度上。
We give a theoretical design for a locally resonant two-dimensional cylindrical structure involving a pair of C-shaped voids in an elastic medium which we term as double 'C' resonators (DCRs) and imbedded thin stiff bars, that displays the negative refraction effect in the low frequency regime. DCRs are responsible for a low frequency band gap which hybridizes with a tiny gap associated with the presence of the thin bars. Using an asymptotic analysis, typical working frequencies are given in closed form: DCRs behave as Helmholtz resonators modeled by masses connected to clamped walls by springs on either side, while thin bars behave as a periodic bi-atomic chain of masses connected by springs. The discrete models give an accurate description of the location and width of the stop band in the case of the DCR and the first two dispersion bands for the periodic thin bars. We then combine our asymptotic formulae for arrays of DCR and thin-bars to design a composite structure that displays a negative refraction effect and has a negative phase velocity in a frequency band, and thus behaves in many ways as a negative refractive acoustic medium (NRAM). Finite element computations show that at this frequency, a slab of such NRAM works as a phononic flat superlens whereas two corners of such NRAM sharing a vertex act as an open resonator and can be used to confine sound to a certain extent.