Scattering of flexural waves by multiple narrow cracks in ice
sheets floating on water
R. Porter & D.V. Evans (submitted)
An explicit solution is derived for the reflection and transmission
of flexural-gravity waves propagating on a uniform elastic ice sheet
floating on water which are obliquely-incident upon any number, N, of
narrow parallel cracks of arbitrary separation. The solution is expressed
in terms of a system of 2N linear equations for the jumps in the
displacements and gradients across each of the cracks. A number of
interesting features of the problem are addressed including the
scattering by periodically-spaced arrays of cracks, the existence of localised
edge wave solutions which travel along each of the cracks and examples of
non-uniqueness, or trapped waves, in the case of four cracks. The problem
of wave reflection by a semi-infinite periodic array of cracks is also
formulated exactly in terms of a convergent infinite system of equations
and relies on certain properties of the so-called Bloch problem for
wave propagation through infinite periodic array of cracks.
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