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Relating the relaxation spectrum to wave dispersion data

Davies, Arthur Russell, Morgan, D. and Williams, P. R. 2004. Relating the relaxation spectrum to wave dispersion data. Journal of non-Newtonian fluid mechanics 124 (1-3) , pp. 25-32. 10.1016/j.jnnfm.2004.07.012

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This paper addresses the problem of determining the relaxation spectrum of a viscoelastic fluid from knowledge of the phase velocity of shear waves propagated in the fluid. Theoretical constraints are obtained which guarantee solvability of the problem. Questions of ill-posedness are identified and it is shown how to include additional information into the problem from independent measurements of group velocity. Alternative integro-differential and integro-algebraic systems are derived which are closed with respect to the original and additional data. A simple iterative algorithm which involves updating estimates of a moment ratio is proposed and tested against two model problems. The algorithm determines an n-mode relaxation spectrum and the corresponding storage and loss moduli.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Relaxation spectrum ; Wave dispersion ; Viscoelastic fluid ; Phase velocity ; Group velocity
Publisher: Elsevier
ISSN: 0377-0257
Last Modified: 04 Jun 2017 01:41

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