Modulated phononic crystals: Non-reciprocal wave propagation and Willis materials
Modulated phononic crystals: Non-reciprocal wave propagation and Willis materials
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DOI：
10.1016/j.jmps.2017.01.010
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发表时间：
2017-04-01
影响因子：
5.3
通讯作者：
Huang, G. L.
中科院分区：
文献类型：
--
作者：
Nassar, H.;Xu, X. C.;Huang, G. L.
波现象中时间反演对称性破缺的研究是声子晶体和超材料领域的一个研究热点，其目的是实现具有许多潜在技术应用的单向传输器件。在这里，我们研究波在声子晶体，特别是周期性层压板，弹性模量和质量密度调制在空间和时间中的波的方式。调制引入了打破时间反演对称性和互易性的偏置。一个完整的表征如何的色散曲线转换，由于波状调制给出了在分析和几何方面的低（亚音速）和高（超音速）的调制速度。理论研究结果得到了数值模拟的支持。更具体的低频率，1，2和3D调制层合板的宏观本构关系被证明是威利斯类型的威利斯耦合在严格的尺度分离的均匀化限制。宏观应力、速度和动量-应变威利斯耦合的存在实际上与互易性的破坏直接相关。最后，得到了宏观本构参数的封闭形式表达式，并导出和讨论了一些基本而有见地的能量界限。(C)2017爱思唯尔有限公司版权所有
Research on breaking time-reversal symmetry in wave phenomena is a growing area of interest in the field of phononic crystals and metamaterials aiming to realize one-way propagation devices which have many potential technological applications. Here we investigate wave propagation in phononic crystals, periodic laminates in particular, where both elastic moduli and mass density are modulated in space and time in a wave-like fashion. The modulation introduces a bias which breaks time-reversal symmetry and reciprocity. A full characterization of how the dispersion curve transforms due to wave-like modulations is given in analytical and geometrical terms for both low (subsonic) and high (supersonic) modulation speeds. Theoretical findings are supported by numerical simulations. More specific to low frequencies, the macroscopic constitutive law of 1, 2 and 3D modulated laminates is proven to be of the Willis type with a non-negligible Willis coupling in the strictly scale-separated homogenization limit. The existence of a macroscopic stress velocity and momentum-strain Willis coupling is in fact directly related to the breaking of reciprocity. Finally, closed form expressions of the macroscopic constitutive parameters are obtained and some elementary yet insightful energy bounds are derived and discussed. (C) 2017 Elsevier Ltd. All rights reserved.