Rogerson, GA, Andrianov, I and Danishevskyy, VV (2018) Elastic Waves in Periodically Heterogeneous Two-dimensional Media: Locally Periodic and Anti-periodic Modes. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474 (2215). ISSN 1471-2946

[thumbnail of 2D anti-periodic paper - R2.pdf]
2D anti-periodic paper - R2.pdf - Accepted Version

Download (728kB) | Preview


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 can be periodic or anti-periodic across the unit cell. It is shown that combining periodicity and anti-periodicity conditions in different directions of the translational symmetry allows one to detect different types of modes that do not arise in the purely periodic case. Such modes may be interpreted as counterparts of non-classical waves appearing in phenomenological theories. Dispersion diagrams of the discrete square lattice are evaluated in a closed analytical from. Dispersion properties of the fibrous medium are determined using Floquet-Bloch theory and Fourier series approximations. Influence of a viscous damping is taken into account.

Item Type: Article
Additional Information: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via The Royal Society at - please refer to any applicable terms of use of the publisher.
Uncontrolled Keywords: wave propagation, heterogeneous medi, phononic bands, dispersion, Floquet-Bloch waves, gradient elasticity, Biot’s theory
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 05 Jul 2018 15:02
Last Modified: 28 Aug 2018 12:43

Actions (login required)

View Item
View Item