Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I - formal solution

Thompson, Ian and Abrahams, I. David (2005) Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I - formal solution. Proceedings of the Royal society A, 461 (2063). pp. 3413-3436. ISSN 1471-2946

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Abstract

The problem of flexural wave diffraction by a semi-infinite crack in an infinite orthotropic thin plate is considered. Such models have application to the ultrasonic non-destructive inspection of thin components, such as aeroplane wings. For simplicity, the plate is modelled using Kirchhoff theory, and the crack is chosen to be aligned along one of the principal directions of material orthotropy. For incident plane waves, an exact analytical expression for the scattered field is derived by means of the Wiener–Hopf technique. In this model problem, the Wiener–Hopf kernel is scalar and its factorization is expressed in terms of simple, definite, non-singular contour integrals. A detailed numerical evaluation of the solution will be provided in the second part of this work.

Item Type: Article
Uncontrolled Keywords: orthotropic plate, thin elastic plate, diffraction, scattering, crack, Wiener–Hopf technique
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 45 Integral equations
MSC 2010, the AMS's Mathematics Subject Classification > 47 Operator theory
Depositing User: Ms Lucy van Russelt
Date Deposited: 22 Mar 2007
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/712

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