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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/11376

Title: Analytical techniques for acoustic scattering by arrays of cylinders
Authors: Tymis, Nikolaos
Keywords: Acoustic
Issue Date: 2012
Publisher: © Nikolaos Tymis
Abstract: The problem of two-dimensional acoustic scattering of an incident plane wave by a semi-infinite lattice is solved. The problem is first considered for sound-soft cylinders whose size is small compared to the wavelength of the incident field. In this case the formulation leads to a scalar Wiener--Hopf equation, and this in turn is solved via the discrete Wiener--Hopf technique. We then deal with a more complex case which arises either by imposing Neumann boundary condition on the cylinders' surface or by increasing their radii. This gives rise to a matrix Wiener--Hopf equation, and we present a method of solution that does not require the explicit factorisation of the kernel. In both situations, a complete description of the far field is given and a conservation of energy condition is obtained. For certain sets of parameters (`pass bands'), a portion of the incident energy propagates through the lattice in the form of a Bloch wave. For other parameters (`stop bands' or `band gaps'), no such transmission is possible, and all of the incident field energy is reflected away from the lattice.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
Version: Not specified
URI: https://dspace.lboro.ac.uk/2134/11376
Appears in Collections:PhD Theses (Maths)

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