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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Diffraction in Mindlin plates - Ian Thompson (Univ
ersity of Liverpool)
DTSTART;TZID=Europe/London:20190816T113000
DTEND;TZID=Europe/London:20190816T120000
UID:TALK128683AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128683
DESCRIPTION:Plate theory is important for modelling thin compo
nents used in engineering applications\, such as m
etal panels used in aeroplane wings and submarine
hulls. A typical application is nondestructive tes
ting\, where a wave is transmitted into a panel\,
and analysis of the scattered response is used to
determine the existence\, size and location of cra
cks and other defects. To use this technique\, one
must first develop a clear theoretical understand
ing the diffraction patterns that occur when a wav
e strikes the tip of a fixed or free boundary. Dif
fraction by semi-infinite rigid strips and cracks
in isotropic plates modelled by Kirchhoff theory w
as considered by Norris &\; Wang(1994). Althoug
h both problems require the application of two bou
ndary conditions on the rigid or free boundary\, t
he resulting Wiener-Hopf equations can be decouple
d\, leading to a pair of scalar problems. Later\,
Thompson &\; Abrahams (2005 &\; 2007) consid
ered diffraction caused by a crack in a fibre rein
forced Kirchhoff plate. The resulting problem is m
uch more complicated than the corresponding isotro
pic case\, but again leads to two separate\, scala
r Wiener-Hopf equations. In this presentation\, we
consider diffraction by rigid strips and cracks i
n plates modelled by Mindlin theory. This is a mor
e accurate model\, which captures physics that is
neglected by Kirchhoff theory\, and is valid at hi
gher frequencies. However\, it requires three boun
dary conditions at an interface. The crack problem
and the rigid strip problem each lead to one scal
ar Wiener-Hopf equation and one 2x2 matrix equatio
n (four problems in total). The scalar problems ca
n be solved in a relatively straightforward manner
\, but the matrix problems (particularly the probl
em for the crack) are complicated. However\, the k
ernels have some interesting properties that sugge
st the possibility of accurate approximate factori
sations.

References

A. N. Norr
is and Z. Wang. Bending-wave diffraction from stri
ps and cracks on thin plates. \;Q. J. Mech. Ap
pl. Math.\, 47:607-627\, 1994.

I. Thompson and
I. D. Abrahams. Diffraction of flexural waves by c
racks in orthotropic thin elastic plates.I Formal
solution. Proc. Roy. Soc. Lond.\, A\, 461:3413-343
4\, 2005.

I. Thompson and I. D. Abrahams. Diffr
action of flexural waves by cracks in orthotropic
thin elastic plates.II. Far field analysis. Proc.
Roy. Soc. Lond.\, A\, 463:1615-1638\, 2007.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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