Dispersion properties of vortex-type monatomic lattices

•Dispersive waves in an elastic two-dimensional chiral lattice are studied.•Chirality is conferred on the medium by gyros connected to the lattice particles.•Standing waves at the critical points of the dispersion surfaces are examined.•Polarisation and wave directionality induced by the gyros are a...

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Bibliographic Details
Published in:International journal of solids and structures 2014-06, Vol.51 (11-12), p.2213-2225
Main Authors: Carta, G., Brun, M., Movchan, A.B., Movchan, N.V., Jones, I.S.
Format: Article
Language:English
Subjects:
Chirality
Dispersion
Dispersions
Dynamic anisotropy
Dynamical systems
Dynamics
Elastic lattice
Gyroscope
Gyroscopes
Lattices
Mathematical models
Rotational
Sound waves
Wave polarisation
Wave propagation
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Summary:•Dispersive waves in an elastic two-dimensional chiral lattice are studied.•Chirality is conferred on the medium by gyros connected to the lattice particles.•Standing waves at the critical points of the dispersion surfaces are examined.•Polarisation and wave directionality induced by the gyros are analysed.•Numerical simulations show dynamic anisotropy, wave polarisation and localisation. The paper presents a systematic study of dispersive waves in an elastic chiral lattice. Chirality is introduced through gyroscopes embedded into the junctions of a doubly periodic lattice. Bloch–Floquet waves are assumed to satisfy the quasi-periodicity conditions on the elementary cell. New features of the system include degeneracy due to the rotational action of the built-in gyroscopes and polarisation leading to the dominance of shear waves within a certain range of values of the constant characterising the rotational action of the gyroscopes. Special attention is given to the analysis of Bloch–Floquet waves in the neighbourhoods of critical points of the dispersion surfaces, where standing waves of different types occur. The theoretical model is accompanied by numerical simulations demonstrating directional localisation and dynamic anisotropy of the system.
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2014.02.026