Assier, Raphael and Peake, Nigel
(2012)
*On the diffraction of acoustic waves by a quarter-plane.*
Wave Motion, 49 (1).
pp. 64-82.

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## Abstract

This paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shaninâ��s theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Greenâ��s functions, leads to three modified Smyshlyaev formulae, which partially solve the far-field problem of scattering of an incident plane wave by a quarter-plane in the Dirichlet case. In this paper, we present similar formulae in the Neumann case, and describe a numerical method allowing a fast computation of the diffraction coefficient using Shaninâ��s third modified Smyshlyaev formula. The method requires knowledge of the eigenvalues of the Laplaceâ��Beltrami operator on the unit sphere with a cut, and we also describe a way of computing these eigenvalues. Numerical results are given for different directions of incident plane wave in the Dirichlet and the Neumann cases, emphasising the superiority of the third modified Smyshlyaev formula over the other two.

Item Type: | Article |
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Uncontrolled Keywords: | Quarter-plane Acoustics Diffraction Far-field |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 30 Functions of a complex variable MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 44 Integral transforms, operational calculus MSC 2010, the AMS's Mathematics Subject Classification > 78 Optics, electromagnetic theory PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 43 Acoustics |

Depositing User: | Dr Raphael Assier |

Date Deposited: | 08 Dec 2014 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2206 |

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