Trapped modes due to narrow cracks in thin simply-supported elastic plates

Richard Porter, David V Evans

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)
359 Downloads (Pure)


We consider an elastic plate of infinite length and constant width supported
simply along its two parallel edges and having a finite length crack along its
centreline. In particular, we look for and find trapped modes (localised oscillations)
in the presence of the crack. An explicit wide-spacing approximation
based on the Wiener-Hopf technique applied to incident wave scattering by
semi-infinite cracks is complemented by an exact formulation of the problem
in the form of integro-differential equations. An application of a Galerkin
method for the numerical calculation of results from the latter method leads
to a novel explicit ‘small-spacing’ approximation. In combination with the
wide-spacing results this is shown to provide accurate results for all lengths
of crack.
Original languageEnglish
Pages (from-to)533–546
Number of pages14
JournalWave Motion
Issue number3
Early online date15 Jan 2014
Publication statusPublished - Apr 2014


  • trapped modes
  • thin elastic plates
  • thin cracks
  • Wiener-Hopf method
  • integro-differential equations


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