Craster, RV, Joseph, LM and Kaplunov, J (2014) Long-wave asymptotic theories: the connection between functionally graded waveguides and periodic media. Wave Motion, 51 (4). 581 - 588.

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Abstract

This article explores the deep connections that exist between the mathematical representations of dynamic phenomena in functionally graded waveguides and those in periodic media. These connections are at their most obvious for low-frequency and long-wave asymptotics where well established theories hold. However, there is also a complementary limit of high-frequency long-wave asymptotics corresponding to various features that arise near cut-off frequencies in waveguides, including trapped modes. Simultaneously, periodic media exhibit standing wave frequencies, and the long-wave asymptotics near these frequencies characterise localised defect modes along with other high-frequency phenomena. The physics associated with waveguides and periodic media are, at first sight, apparently quite different, however the final equations that distill the essential physics are virtually identical. The connection is illustrated by the comparative study of a periodic string and a functionally graded acoustic waveguide.

Item Type: Article
Uncontrolled Keywords: asymptotic, low-frequency, high-frequency, homogenisation, waveguide, functionally graded,
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 26 Feb 2016 09:15
Last Modified: 20 May 2019 11:00
URI: http://eprints.keele.ac.uk/id/eprint/1495

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