 
Summary: Diffraction of flexural waves by cracks
in orthotropic thin elastic plates. I
Formal solution
BY IAN THOMPSON AND I. DAVID ABRAHAMS
School of Mathematics, University of Manchester,
Oxford Road, Manchester M13 9PL, UK
(dabrahams@ma.man.ac.uk)
The problem of flexural wave diffraction by a semiinfinite crack in an infinite orthotropic
thin plate is considered. Such models have application to the ultrasonic nondestructive
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 WienerHopf technique. In
this model problem, the WienerHopf kernel is scalar and its factorization is expressed in
terms of simple, definite, nonsingular contour integrals. A detailed numerical evaluation
of the solution will be provided in the second part of this work.
Keywords: orthotropic plate; thin elastic plate; diffraction; scattering; crack;
WienerHopf technique
1. Introduction
There is considerable interest in the ultrasonic nondestructive evaluation of thin
