## 2014.60: On the diffraction of acoustic waves by a quarter-plane

2014.60:
Raphael Assier and Nigel Peake
(2012)
*On the diffraction of acoustic waves by a quarter-plane.*
Wave Motion, 49 (1).
pp. 64-82.

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 1894 Kb |

DOI: 10.1016/j.wavemoti.2011.07.003

## Abstract

This paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shanin’s theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Green’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 Shanin’s third modified Smyshlyaev formula. The method requires knowledge of the eigenvalues of the Laplace–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 |
---|---|

Uncontrolled Keywords: | Quarter-plane Acoustics Diffraction Far-field |

Subjects: | MSC 2000 > 30 Functions of a complex variable MSC 2000 > 35 Partial differential equations MSC 2000 > 44 Integral transforms, operational calculus MSC 2000 > 78 Optics, electromagnetic theory PACS 2003 > 43 Acoustics |

MIMS number: | 2014.60 |

Deposited By: | Dr Raphael Assier |

Deposited On: | 08 December 2014 |

Download Statistics: last 4 weeks

Repository Staff Only: edit this item