Scattering by a semi-infinite lattice and the excitation of Bloch waves



Tymis, N and Thompson, I ORCID: 0000-0001-5537-450X
(2014) Scattering by a semi-infinite lattice and the excitation of Bloch waves. The Quarterly Journal of Mechanics and Applied Mathematics, 67 (3). pp. 469-503.

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Abstract

The interaction of a time-harmonic plane wave with a semi-infinite lattice of identical circular cylinders is considered, using a formulation that allows for cylinders of finite size that do not scatter isotropically. Multipole expansions and Graf's addition theorem are used to reduce the boundary value problem to an infinite linear system of equations. Applying the z transform and disregarding interaction effects due to certain strongly damped modes then leads to a matrix Wiener–Hopf equation with rational elements. This is solved by a straightforward method that does not require matrix factorisation. Implementation of the method requires that the zeros of the matrix determinant be located numerically, and once this is achieved, all far-field quantities can be calculated. Numerical results that show the proportion of energy reflected back from the edge are presented for several different lattice geometries.

Item Type: Article
Additional Information: 31 pages. First published online June 26, 2014
Subjects: ?? QA ??
Divisions: Faculty of Science and Engineering > School of Physical Sciences > Mathematical Sciences
Depositing User: Symplectic Admin
Date Deposited: 06 Nov 2013 12:35
Last Modified: 15 Dec 2022 12:41
DOI: 10.1093/qjmam/hbu014
Publisher's Statement : © Oxford University Press 2013
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/13973