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SUMMARY:Diffraction in Mindlin plates - Ian Thompson (University of Liverp
 ool)
DTSTART:20190816T103000Z
DTEND:20190816T110000Z
UID:TALK128686@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Plate theory is important for modelling thin components used i
 n engineering applications\, such as metal panels used in aeroplane wings 
 and submarine hulls. A typical application is nondestructive testing\, whe
 re a wave is transmitted into a panel\, and analysis of the scattered resp
 onse is used to determine the existence\, size and location of cracks and 
 other defects. To use this technique\, one must first develop a clear theo
 retical understanding the diffraction patterns that occur when a wave stri
 kes the tip of a fixed or free boundary. Diffraction by semi-infinite rigi
 d strips and cracks in isotropic plates modelled by Kirchhoff theory was c
 onsidered by Norris &amp\; Wang(1994). Although both problems require the 
 application of two boundary conditions on the rigid or free boundary\, the
  resulting Wiener-Hopf equations can be decoupled\, leading to a pair of s
 calar problems. Later\, Thompson &amp\; Abrahams (2005 &amp\; 2007) consid
 ered diffraction caused by a crack in a fibre reinforced Kirchhoff plate. 
 The resulting problem is much more complicated than the corresponding isot
 ropic case\, but again leads to two separate\, scalar Wiener-Hopf equation
 s. In this presentation\, we consider diffraction by rigid strips and crac
 ks in plates modelled by Mindlin theory. This is a more accurate model\, w
 hich captures physics that is neglected by Kirchhoff theory\, and is valid
  at higher frequencies. However\, it requires three boundary conditions at
  an interface. The crack problem and the rigid strip problem each lead to 
 one scalar Wiener-Hopf equation and one 2x2 matrix equation (four problems
  in total). The scalar problems can be solved in a relatively straightforw
 ard manner\, but the matrix problems (particularly the problem for the cra
 ck) are complicated. However\, the kernels have some interesting propertie
 s that suggest the possibility of accurate approximate factorisations.<br>
  <br> <br><br>References<br>A. N. Norris and Z. Wang. Bending-wave diffrac
 tion from strips and cracks on thin plates.&nbsp\;Q. J. Mech. Appl. Math.\
 , 47:607-627\, 1994.<br>I. Thompson and I. D. Abrahams. Diffraction of fle
 xural waves by cracks in orthotropic thin elastic plates.I Formal solution
 . Proc. Roy. Soc. Lond.\, A\, 461:3413-3434\, 2005.<br>I. Thompson and I. 
 D. Abrahams. Diffraction of flexural waves by cracks in orthotropic thin e
 lastic plates.II. Far field analysis. Proc. Roy. Soc. Lond.\, A\, 463:1615
 -1638\, 2007.
LOCATION:Seminar Room 1\, Newton Institute
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