Scattering of elastic waves by a small inclined surface-breaking crack |
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Authors: | I D Abrahams |
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Institution: | Department of Mathematics, Keele University, Keele, Staffs, ST5 5BG, U.K. Department of Mathematics, The University of Manchester, Manchester M13 9PL, U.K. |
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Abstract: | I
we examine the scattering of Rayleigh waves by an inclined two-dimensional plane surface-breaking crack in an isotropic elastic half-plane. We follow the method already introduced by the authors (A
and W
, 1992a, J. Mech. Phys. Solids 40, 1683) to obtain an analytical solution when the parameter , which is the ratio of a typical length scale of the imperfection to the incident radiation's wavelength, is small. The procedure employed is the method of matched asymptotic expansions, which involves determining the scattered wave field both away from and near the crack. The outer solution is specialized from the general expansion in the first part of this work (A
and W
, 1992a, J. Mech. Phys. Solids 40, 1683), and the inner problem is exactly solved by the Wiener-Hopf technique. The displacement field and scattered Rayleigh waves are found uniformly to third order in , and concluding remarks are made about the general method as well as the results presented here. |
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Keywords: | |
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