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http://bura.brunel.ac.uk/handle/2438/4334
Title: | Asymptotic equivalence of homogenisation procedures and fine-tuning of continuum theories |
Authors: | Pichugin, AV Askes, H Tyas, A |
Issue Date: | 2008 |
Publisher: | Elsevier |
Citation: | Journal of Sound and Vibration. 313(3–5): 858–874 |
Abstract: | Long-wave models obtained in the process of asymptotic homogenisation of structures with a characteristic length scale are known to be non-unique. The term non-uniqueness is used here in the sense that various homogenisation strategies may lead to distinct governing equations that usually, for a given order of the governing equation, approximate the original problem with the same asymptotic accuracy. A constructive procedure presented in this paper generates a class of asymptotically equivalent long-wave models from an original homogenised theory. The described non-uniqueness manifests itself in the occurrence of additional parameters characterising the model. A simple problem of long-wave propagation in a regular one-dimensional lattice structure is used to illustrate important criteria for selecting these parameters. The procedure is then applied to derive a class of continuum theories for a two-dimensional square array of particles. Applications to asymptotic structural theories are also discussed. In particular, we demonstrate how to improve the governing equation for the Rayleigh-Love rod and explain the reasons for the well-known numerical accuracy of the Mindlin plate theory. |
URI: | http://bura.brunel.ac.uk/handle/2438/4334 |
DOI: | http://dx.doi.org/10.1016/j.jsv.2007.12.005 |
ISSN: | 0022-460X |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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2008jsv.pdf | 378.11 kB | Adobe PDF | View/Open |
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