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SIAM J. on Applied Mathematics / Volume 67 / Issue 5

SIAM J. Appl. Math. 67, pp. 1233-1258 (26 pages)

Scattering by a Semi-Infinite Periodic Array and the Excitation of Surface Waves

C. M. Linton, R. Porter, and I. Thompson

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The two-dimensional problem of acoustic scattering of an incident plane wave by a semi-infinite array of either rigid or soft circular scatterers is solved. Solutions to the corresponding infinite array problems are used, together with a novel filtering approach, to enable accurate solutions to be computed efficiently. Particular attention is focused on the determination of the amplitude of the Rayleigh–Bloch waves that can be excited along the array. In general, the far field away from the array consists of the sum of a finite number of plane waves propagating in different directions (the number depending on the observation angle) and a circular wave emanating from the edge of the array. In certain resonant cases (characterized by one of the scattered plane waves propagating parallel to the array), a different far field pattern occurs, involving contributions that are neither circular waves nor plane waves. Uniform asymptotic expansions that vary continuously across all of the shadow boundaries that exist are given for both cases.

© 2007 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

74J20, 74J15, 78A45

PUBLICATION DATA

ISSN

0036-1399 (print)  
1095-712X (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received October 18, 2006
Accepted February 16, 2007
Published online June 15, 2007
Digital Object Identifier
http://dx.doi.org/10.1137/060672662

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