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Cubic-symmetry acoustic metamaterials with roton-like dispersion relations

具有类roton色散关系的立方对称声学超材料

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Abstract

In our previous work, we have shown that nonlocal interactions in acoustic metamaterials can lead to highly unusual roton-like dispersion relations exhibiting a minimum of frequency versus wavenumber similar to that of superfluid Helium-4. However, this behavior was limited to only one or two propagation directions of sound. Here, we design a three-dimensional cubic-symmetry airborne acoustic metamaterial with nonlocal interactions along three orthogonal directions. By using numerical finite-element calculations, we show that the metamaterial supports roton-like behavior along all three orthogonal directions, but the behavior is far from isotropic. We compare these calculations with a simplified semi-analytical model, leading to good overall agreement. Corresponding experiments appear in reach, but are demanding due to the required dense and complex three-dimensional network of acoustic channels that connect compartments of air.

摘要

我们之前的工作表明, 声学超材料中的非局部相互作用会导致极不寻常的类roton色散关系, 即色散曲线存在局部极小值, 与超 流体液氦-4类似. 然而, 这种行为仅限于一个或两个声传播方向. 在这里, 我们设计了一种三维立方对称声学超材料, 沿三个正交方向具 有非局部相互作用. 有限元计算表明超材料在三个正交方向具有类roton行为, 但其行为远非各向同性. 有限元结果与半解析模型结果 吻合良好. 相应的实验正在探索中, 由于需要密集而复杂的三维声学管道, 实验要求较高.

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Acknowledgements

Ke Wang acknowledges support by the China Scholarship Council (CSC). This research has additionally been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy via the Excellence Cluster “3D Matter Made to Order” (Grant No. EXC-2082/1-390761711), which has also been supported by the Carl Zeiss Foundation through the “Carl-Zeiss-Foundation-Focus@HEiKA”, by the State of Baden-Württemberg, and by the Karlsruhe Institute of Technology (KIT). We further acknowledge support by the Helmholtz program “Materials Systems Engineering” (MSE). Muamer Kadic is grateful for support by the EIPHI Graduate School (Grant No. ANR-17-EURE-0002). Changguo Wang is grateful for support by the National Natural Science Foundation of China (Grant No. 12172102).

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Authors and Affiliations

  1. National Key Laboratory of Science and Technology on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin, 150001, China

    Ke Wang  (王珂) & Changguo Wang  (王长国)

  2. Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), Karlsruhe, 76128, Germany

    Ke Wang  (王珂), Yi Chen  (陈毅) & Martin Wegener

  3. Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Karlsruhe, 76128, Germany

    Yi Chen  (陈毅) & Martin Wegener

  4. Institut FEMTO-ST, UMR 6174, CNRS, Université de Franche-Comté, Besançon, 25030, France

    Muamer Kadic

Authors
  1. Ke Wang  (王珂)
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  2. Yi Chen  (陈毅)
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  3. Muamer Kadic
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  4. Changguo Wang  (王长国)
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  5. Martin Wegener
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Contributions

Author contributions Ke Wang and Yi Chen performed the numerical simulations and theoretical derivations. Ke Wang and Muamer Kadic designed the metamaterials. Yi Chen and Martin Wegener wrote the first draft. Changguo Wang and Martin Wegener supervised the effort. All authors discussed the results and contributed to the writing and reviewing of the manuscript.

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Correspondence to Ke Wang  (王珂).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Wang, K., Chen, Y., Kadic, M. et al. Cubic-symmetry acoustic metamaterials with roton-like dispersion relations. Acta Mech. Sin. 39, 723020 (2023). https://doi.org/10.1007/s10409-023-23020-x

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  • DOI: https://doi.org/10.1007/s10409-023-23020-x

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