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Some comments on the dispersion relation for periodically layered pre-stressed elastic media

Rogerson, GA and Sandiford, KJ 2002, 'Some comments on the dispersion relation for periodically layered pre-stressed elastic media' , International Journal of Engineering Science, 40 (1) , pp. 23-49.

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Abstract

In this paper the dispersion relation associated with harmonic waves propagating in a periodically layered structure is derived and analysed. Specifically, the structure is made up of repeating unit cells, with each layer composed of an incompressible, pre-stressed elastic material, each interface perfectly bonded and the upper and lower surfaces of the structure free of incremental traction. The complexity of the problem is reduced using an approach involving the Cayley-Hamilton theorem. A numerical method is also used which eliminates positive exponential functions, thereby considerably reducing the complexity of solving the dispersion relation numerically. Numerical solutions are presented in respect of both a two-ply and symmetric four-ply unit cell. An interesting feature of these solutions is the grouping together of harmonics as the number of unit cells increases. In the case of n unit cells, n-1 harmonics group together in the moderate wave number region, with an additional harmonic joining the group at a higher wave number.

Item Type: Article
Themes: Subjects / Themes > Q Science > QA Mathematics
Subjects outside of the University Themes
Schools: Colleges and Schools > College of Science & Technology
Colleges and Schools > College of Science & Technology > School of Computing, Science and Engineering
Colleges and Schools > College of Science & Technology > School of Computing, Science and Engineering > Materials & Physics Research Centre
Journal or Publication Title: International Journal of Engineering Science
Publisher: Elsevier
Refereed: Yes
ISSN: 00207225
Depositing User: H Kenna
Date Deposited: 23 Aug 2007 12:30
Last Modified: 20 Aug 2013 16:47
URI: http://usir.salford.ac.uk/id/eprint/342

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