# 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} }

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…

## 19 Citations

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A novel characterisation of dispersive waves in a vector elastic lattice is presented in the context of wave polarisation. This proves to be especially important in analysis of dynamic anisotropy and…

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An asymptotic approach for overcoming hidden singularities associated with band-gap edges and branch crossings is suggested, which is developed in detail in the case of time-harmonic waves in one dimension.

### Elastic waves in periodically heterogeneous two-dimensional media: locally periodic and anti-periodic modes

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Propagation of anti-plane waves through a discrete square lattice and through a continuous fibrous medium is studied. In the long-wave limit, for periodically heterogeneous structures the solution…

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The paper presents the study of waves in a structured geometrically chiral solid. A special attention is given to the analysis of the Bloch-Floquet waves in a doubly periodic high-contrast lattice…

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