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Wave propagation in two-dimensional anisotropic acoustic metamaterials of K4 topology

journal contribution
posted on 2025-02-14, 10:11 authored by AS Fallah, Y Yang, R Ward, M Tootkaboni, R Brambleby, A Louhghalam, LA Louca
An acoustic metamaterial is envisaged as a synthesised phononic material the mechanical behaviour of which is determined by its unit cell. The present study investigates one aspect of mechanical behaviour, namely the band structure, in two-dimensional (2D) anisotropic acoustic metamaterials encompassing locally resonant mass-in-mass units connected by massless springs in a K4 topology. The 2D lattice problem is formulated in the direct space (r-space) and the equations of motion are derived using the principle of least action (Hamilton's principle). Only proportional anisotropy and attenuation-free shock wave propagation have been considered. Floquet-Bloch's principle is applied, therefore a generic unit cell is studied. The unit cell can represent the entire lattice regardless of its position. It is transformed from the direct lattice in r-space onto its reciprocal lattice conjugate in Fourier space (k-space) and point symmetry operations are applied to Wigner-Seitz primitive cell to derive the first irreducible Brillouin Zone (BZ). The edges of the first irreducible Brillouin Zone in the k-space have then been traversed to generate the full band structure. It was found that the phenomenon of frequency filtering exists and the pass and stop bands are extracted. A follow-up parametric study appreciated the degree and direction of influence of each parameter on the band structure.

History

Refereed

  • Yes

Volume

58

Page range

101-116

Publication title

Wave Motion

ISSN

0165-2125

Publisher

Elsevier BV

File version

  • Published version

Language

  • eng

Item sub-type

Journal Article

Affiliated with

  • School of Engineering and The Built Environment Outputs