Diffraction of flexural waves by finite straight cracks in an elastic
sheet over water.
R. Porter & D.V. Evans, 2005, Journal of Fluids and Structures (submitted)
The diffraction of long-crested incident waves propagating within
a thin flexible elastic sheet floating on water by narrow cracks is
considered. The cracks are straight and each of finite length and
must be parallel to one another. This arrangement lends itself to the use
of Fourier transform methods, which allows the solution to a
simpler problem to be used. For $N$ cracks, $2N$ coupled integral
equations results for $2N$ unknown functions related to the
jump in displacement and slope across each crack as a function of
distance along the cracks. These integral equations are hypersingular,
but in approximating their solution using Galerkin's method, a
judicious choice of trial function provides maximum simplification
in the algebraic equations which result.
Numerical results focus on the diffracted wave amplitudes, the
maximum displacement of the elastic sheet and the stress insensity
factor at the ends of the cracks. For two side-by-side cracks, large
resonant motion can occur in the strip between the cracks.
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