## Abstract

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 focussed on the accurate determination of the amplitude of the Rayleigh-Bloch waves that can be excited along the array. The far-field away from the array is shown to be 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. A uniform asymptotic expansion is derived which varies continuously across the shadow boundaries that exist. We consider resonant (when one wave propagates along or directly away from the array) and non-resonant cases.

Translated title of the contribution | Scattering by a semi-infinite periodic array and excitation of surface waves |
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Original language | English |

Pages (from-to) | 1233 - 1258 |

Number of pages | 26 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 67 (5) |

DOIs | |

Publication status | Published - Jun 2007 |