• DOI:10.1093/QJMAM/HBV005
• Corpus ID: 55463564

High frequency homogenisation for elastic lattices

@article{Colquitt2014HighFH,
  title={High frequency homogenisation for elastic lattices},
  author={D. J. Colquitt and Richard V. Craster and Mehul P. Makwana},
  journal={Quarterly Journal of Mechanics and Applied Mathematics},
  year={2014},
  volume={68},
  pages={203-230}
}

• D. Colquitt, R. Craster, M. Makwana
• Published 8 July 2014
• Physics
• Quarterly Journal of Mechanics and Applied Mathematics

AbstractA complete methodology, based on a two-scale asymptotic approach, that enables the ho-mogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distin-guished from scalar lattices in that two or more types of coupled waves exist, even at low frequen-cies. Such a theory enables the determination of e ective material properties at both low and highfrequencies. The theoretical framework is developed for the propagation of waves through latticesof arbitrary geometry and dimension. The asymptotic approach provides a method through whichthe dispersive properties of lattices at frequencies near standing waves can be described; the theoryaccurately describes both the dispersion curves and the response of the lattice near the edges ofthe Brillouin zone. The leading order solution is expressed as a product between the standingwave solution and long-scale envelope functions that are eigensolutions of the homogenised partialdi erential equation. The general theory is supplemented by a pair of illustrative examples fortwo archetypal classes of two-dimensional elastic lattices. The eciency of the asymptotic ap-proach in accurately describing several interesting phenomena is demonstrated, including dynamicanisotropy and Dirac cones.