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Flexural waves on a pinned semi-infinite thin elastic plate

I. Thompson, C. M. Linton & R. Porter, (submitted, Aug 2007)

The scattering of water waves by a long array of rigid vertical circular
cylinders is analysed under the usual assumptions of linear theory. Our
primary goal is to show how solutions obtained for semi-infinite arrays
can be combined to provide accurate and numerically efficient solutions
to problems involving long, but finite, arrays. The particular diffraction
problem considered here has been chosen both for its theoretical interest
and its applicability. The design of offshore structures supported by
cylindrical columns is commonplace and understanding how the multiple
interactions between the waves and the supports affect the field is
clearly important. The theoretical interest comes from the fact that, for
wavelengths greater than twice the geometric periodicity, the associated
infinite array can support Rayleigh-Bloch surface waves that propagate
along the array without attenuation. For a long finite array we expect
to see these surface waves travelling back and forth along the array
and interacting with the ends. For particular sets of parameters, near
trapping has previously been observed and we provide, for the first time,
a quantitative explanation of this phenomenon based on the excitation
and reflection of surface waves by the ends of the finite array.

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