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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Abstract

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
URI:	https://orca.cardiff.ac.uk/id/eprint/1702

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