On a surface wave along the cylindrical cavity in an inhomogeneous elastic material
DOI:
https://doi.org/10.15407/dopovidi2019.05.024Keywords:
attenuation of a harmonic wave, cylindrical surface, cylindrical surface elastic wave, exponentially inhomogeneous medium, Macdonald functionsAbstract
The classical Biot problem on a surface harmonic elastic wave propagating along the free surface of a cylindrical cavity is generalized to the case of inhomogeneity of a medium of propagation. It is assumed that the density and Lamé elastic parameters of the medium are changed with increasing the radius (they become smaller with moving from the cavity) by the exponential law. The prior results on a general representation of solutions are used. The problem is solved analytically up to the level, when the numerical methods have to be used.
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Biot, M. A. (1952). Propagation of elastic waves in a cylindrical bore containing a fluid. J Appl. Phys., 23, No. 9, pp. 997-1005. doi: https://doi.org/10.1063/1.1702365
Olver, F. W. J., Lozier, D. W., Bousvert, R. F. & Clark, C. W. (eds). (2010). NIST (National Institute of Standards and Technology). Handbook of Mathematical Functions. Cambridge: Cambridge Univ. Press, 968 p.
Achenbach, J. D. (1973). Wave Propagation in Elastic Solids. Amsterdam: North-Holland, 425 p.
Viktorov, I. A. (1967). Rayleigh and Lamb Waves. New York: Plenum Press, 168 p. doi: https://doi.org/10.1007/978-1-4899-5681-1
Rushchitsky, J. J. (2012). Theory of waves in materials. Copenhagen: Ventus Publishing ApS, 270 p.
Rushchitsky, J. J. (2014). Nonlinear Elastic Waves in Materials. Series: Foundations of engineering mechanics. Heidelberg: Springer, 454 p. doi: https://doi.org/10.1007/978-3-319-00464-8
Lekhnitsky, S. G. (1963). Theory of Elasticity of Anisotropic Elastic Body. San Francisco: Golden Day Inc., 404 p. doi: https://doi.org/10.1137/1009023
Kashtalyan, M. & Rushchitsky, J. J. (2009). Revisiting displacement functions in three-dimen sional elasticity of inhomogeneous media. Int. J. Solids Struct., 46, No. 18-19, pp. 3463-3470. doi: https://doi.org/10.1016/j.ijsolstr.2009.06.001
Kashtalyan, M. & Rushchitsky, J. J. (2010). General Love solution in the linear inhomogeneous isotropic theory of elasticity in dependence of elastic properties on radius. Int.Appl. Mech., 46, No. 3, pp. 245-254. doi: https://doi.org/10.1007/s10778-010-0304-6
Kashtalyan, M. & Rushchitsky, J. J. (2010). General Love solution in the linear inhomogeneous transversely isotropic theory of elasticity in dependence of elastic constants on radial coordinate. Int. Appl. Mech., 46, No. 4, pp. 331-343. doi: https://doi.org/10.1007/s10778-010-0304-6
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