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Acoustic scattering from a one-dimensional array; Tail-end asymptotics for efficient evaluation of the quasi-periodic Green's function

Published version
Peer-reviewed

Type

Article

Change log

Authors

Lynott, GM 
Andrew, V 
Abrahams, ID 
Simon, MJ 
Parnell, WJ 

Abstract

© 2019 The Authors Motivated by the problem of acoustic plane wave scattering from an infinite periodic array of cylindrical scatterers, we present a new and easily-implemented way of calculating the quasi-periodic Green's function. This approach is based on an asymptotic expansion of the summand in the quasi-periodic Green's function in order to derive a tail-end correction term, allowing for a rapid and accurate approximation of the function. The tail-end approximation is shown to have much better and faster convergence properties than the usual truncation approach and competes very well with state-of-the-art alternative techniques. This method is then combined with a boundary element scheme to calculate the transmission and reflection coefficients associated with arrays of cylinders of different cross-sections and varying aspect ratios. The results are validated against the existing literature and by independent finite element calculations.

Description

Keywords

Acoustics, Scattering, Quasi-periodic Green's functions, Arrays

Journal Title

Wave Motion

Conference Name

Journal ISSN

0165-2125
1878-433X

Volume Title

89

Publisher

Elsevier BV
Sponsorship
Engineering and Physical Sciences Research Council (EP/K032208/1)
EPSRC grant EP/R014604/1