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Wave attenuation and negative refraction of elastic waves in a single-phase elastic metamaterial

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Abstract

In this paper, we propose and study a single-phase elastic metamaterial with periodic chiral local resonator, which is composed of cylindrical central core surrounded by evenly distributed ligaments and embedded in the matrix in a square lattice. Based on the analytical and numerical analysis, we prove that the translational resonance of the unit cell can lead to negative effective mass density, and the rotational resonance of it can produce negative effective modulus. They can also work together to generate double-negative effective material properties. The wave attenuation of elastic waves in this elastic metamaterial is also demonstrated, which is owing to the negative effective mass density. In addition, the damping of the base material is also considered in the simulation. We finally examine the existence of negative band, and this leads to the physics of negative refraction, which is induced by simultaneous translational and rotational resonance of the unit cell. Our work can serve as the theoretical foundation for the design of single-phase elastic metamaterials.

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Acknowledgements

We appreciate the financial support from the National Natural Science Foundation of China (Grants No. 11402101).

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Authors and Affiliations

  1. Department of System Engineering, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Sheng Sang & Eric Sandgren

  2. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013, China

    Sheng Sang & Ziping Wang

Authors
  1. Sheng Sang
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  2. Eric Sandgren
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  3. Ziping Wang
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Correspondence to Sheng Sang.

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Sang, S., Sandgren, E. & Wang, Z. Wave attenuation and negative refraction of elastic waves in a single-phase elastic metamaterial. Acta Mech 229, 2561–2569 (2018). https://doi.org/10.1007/s00707-018-2127-1

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  • DOI: https://doi.org/10.1007/s00707-018-2127-1

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