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Abstract
The scattering of guided elastic waves from a circumferential crack in an isotropic hollow cylinder is investigated analytically using the S-parameter formalism. A general formula, analogous to that of [B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, Malabar, FL, 1990), 2nd ed., Vol. II, p. 200], is derived for the scattered amplitude of an arbitrary mode due to the incidence of an arbitrary mode. The amplitudes are expressed as an integral of the inner product of the crack opening displacement caused by the incident mode and the traction field of the scattered mode. Using a simple approximate form of known elastostatic solutions for the crack opening displacements due to pure tension, a formula is derived for the scattering of guided wave modes of arbitrary circumferential order due to the incidence of axisymmetric wave modes with large wavelength and uniform stress distribution. These results are analyzed and conclusions drawn on the possibility of crack sizing using relatively simple scattering amplitude information.
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