Abstract
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.
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 language | English |
|---|---|
| Pages (from-to) | 533–546 |
| Number of pages | 14 |
| Journal | Wave Motion |
| Volume | 51 |
| Issue number | 3 |
| Early online date | 15 Jan 2014 |
| DOIs | |
| Publication status | Published - Apr 2014 |
Keywords
- trapped modes
- thin elastic plates
- thin cracks
- Wiener-Hopf method
- integro-differential equations