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Waves in Structured Mediums or Metamaterials: A Review

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Abstract

Wave propagation through a structured medium has attracted the attention of researchers for centuries due to its relevance to problems in condensed matter physics, chemistry, optics, phononics, composite, acoustics and mechanics. Wave containing certain band of frequencies can either propagate, known as transmission, or attenuated, known as attenuation band. This band structure for a continuum and its equivalent lumped spring mass model are not identical, although continuum medium is often modelled as a chain of discrete periodic structures because the continuous and discrete is depends on the scale. These band characteristics are dependent on the properties of the units, thus the effects of different parameters, such as damping, stiffness and mass ratios, nonlinearity, on the bandwidth are compared with each other in this review. To cloak, modulate, guide, filter out or attenuate unwanted frequencies from the propagating waves, metamaterials are widely investigated as a special form of the periodic structures from the past 2 decades. The main aim of this review is to compare the bandwidth for one-dimensional periodic structures. Waves through two and three-dimensional periodic medium are not considered in the review because the key band characteristics of periodic system can be perceived in one dimensional. The methods for computing the wave transmission are evaluated in the non-dimensional domain and the band characteristics of different one-dimensional periodic structures are critically assessed in this review. This review will help to the future researchers to choose a proper periodic medium for getting a specific band phenomenon.

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Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Auckland, 20 Symonds Street, Auckland, 1010, New Zealand

    Arnab Banerjee

  2. Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, Kanpur, Uttar Pradesh, 208016, India

    Arnab Banerjee

  3. Sir Lawrence Wackett Aerospace Research Centre, School of Engineering, RMIT University, GPO Box 2476, Melbourne, VIC, 3001, Australia

    Raj Das

  4. Advanced Materials Group, Research and Technical Services, Callaghan Innovation, 24 Balfour Rd, Parnell, Auckland, 1052, New Zealand

    Emilio P. Calius

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  1. Arnab Banerjee
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  2. Raj Das
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Correspondence to Arnab Banerjee.

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Banerjee, A., Das, R. & Calius, E.P. Waves in Structured Mediums or Metamaterials: A Review. Arch Computat Methods Eng 26, 1029–1058 (2019). https://doi.org/10.1007/s11831-018-9268-1

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