We have solved the problem of determination of the stressed state in an isotropic elastic body near ring-shaped defects (a crack or a thin rigid inclusion) as a result of the action of a harmonic torsional wave. The method of solution is based on the use of discontinuous solutions of the equation of torsional vibrations and lies in the reduction of the initial boundary-value problems to integral equations for the unknown jumps of angular displacement or tangential stress.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 2, pp. 109–117, April–June, 2009.
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Varvarets’ka, H.A., Popov, V.H. Interaction of a harmonic torsional wave with ring-shaped defects in an elastic body. J Math Sci 170, 695–707 (2010). https://doi.org/10.1007/s10958-010-0114-8
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DOI: https://doi.org/10.1007/s10958-010-0114-8