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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.

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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

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