Scattering by small defects in the neighbourhood of a fluid-solid interface |
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Authors: | Williams DP; Craster RV |
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Institution: |
Z Department of Theoretical Mechanics, University of Nottingham, Nottingham NG7 2RD, UK ZZ Department of Mathematics, Imperial College of Science, Technology and Medicine, London SW7 2BZ, UK
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Abstract: | The scattering of incident plane elastic waves by a varietyof different defects that lie upon a fluid-solid interface isconsidered here using matched asymptotic expansions. The expansionscheme is developed in terms of a parameter , the ratio of typicaldefect length scale to a typical wavelength of the incidentfield, taken to be small. Three different canonical situations occur and these are illustratedvia three specific examples treated here: a rigid strut, anedge crack, and a rigid strip. In each case the leading-ordermatching is performed to identify the leading-order contributionof the defect to the acoustic field in the far field. In particular,each defect is identified with a source of dipole response ininterfacial stress of displacement. It is shown in the limit as s<<s1 that in the inner problemsthe fluid and solid pieces uncouple in a particularly convenientmanner allowing analytical solutions to be deduced. These arethen matched with appropriate outer solutions. |
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