We solve the problem of the diffraction of an elastic SH-wave on an interface crack that was formed on the boundary of the perfectly rigid joint of a plate with a half-space. Semiinfinite and finite cracks are considered. We obtain a solution of the diffraction problem for a semiinfinite crack in the analytic form by using the Wiener–Hopf technique. In the case of a finite crack, the problem is reduced to the solution of an infinite system of linear algebraic equations. We investigate the coefficients of wave transformation at the tip of a semiinfinite interface crack. In the case of a finite crack, we obtain the eigenvalues of the operator of the diffraction problem, which determine the complex resonance frequencies of the dynamical system. We also present the dependence of eigenfrequencies and natural vibrations on the structure parameters.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 2, pp. 107–118, April–June, 2012.
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Nazarchuk, Z.T., Kuryliak, D.B., Voytko, M.V. et al. On the interaction of an elastic SH-wave with an interface crack in the perfectly rigid joint of a plate with a half-space. J Math Sci 192, 609–622 (2013). https://doi.org/10.1007/s10958-013-1420-8
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DOI: https://doi.org/10.1007/s10958-013-1420-8