The problem of oblique wave scattering of a Rayleigh wave by a cylindrical cavity
in an elastic half-space is solved using the multipole expansion method. Whereas in the
analogous water-wave problem a single scalar field is expressed as an infinite multipole
expansion, and in the Rayleigh wave case with normal incidence two scalar fields suffice,
here we require three coupled scalar multipole expansions. The focus of our numerical
results is on the energy scattered by the cavity and in particular the proportion of the
incident wave energy that is reflected and transmitted in the form of Rayleigh waves
and the proportion that is transformed into cylindrical bulk waves which propagate
into the half-space.
Published inThe Quarterly Journal of Mechanics and Applied Mathematics
Pages235 - 261
CitationLINTON, C.M. and THOMPSON, I., 2015. Oblique Rayleigh wave scattering by a cylindrical cavity. Quarterly Journal of Mechanics and Applied Mathematics, 68(3), pp. 235-261.
Publisher© Oxford University Press.
VersionAM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis is a pre-copyedited, author-produced PDF of an article accepted for publication in Quarterly Journal of Mechanics and Applied Mathematics following peer review. The version of record LINTON, C.M. and THOMPSON, I., 2015. Oblique Rayleigh wave scattering by a cylindrical cavity. Quarterly Journal of Mechanics and Applied Mathematics, 68(3), pp. 235-261 is available online at: http://dx.doi.org/10.1093/qjmam/hbv006