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Behavior of surface waves at transition through a junction line on the boundary of an elastic homogenous isotropic body

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Abstract

A homogeneous elastic body with stress-free boundary is considered. The boundary of the body, which consists of a smooth cylindrical surface and a half-plane, has a continuous tangent plane, but the curvature of the normal section of the boundary has a discontinuity of the first kind at each point of the junction line. The behavior of two kinds of “whispering gallery” transversal surface waves at transition through the junction line is studied. For waves of the first kind (corresponding to Dirichlet boundary conditions), the displacement vector is normal to the boundary, whereas for waves of the second kind (corresponding to Neumann boundary conditions) the displacement vector is tangent to the boundary and normal to the ray, similarly to the case of Love waves. Bibliography: 4 titles.

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References

  1. N. Ya. Kirpichnikova, “Propagation of surface waves concentrated near rays in an inhomogeneous elastic body of arbitrary shape,”Trudy Math. Inst. Akad. Nauk SSSR,115, 127–145 (1971).

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  2. V. M. Babich and N. Ya. Kirpichnikova, “On the propagation of Love waves along the surface of an elastic nonhomogenous body of arbitrary shape,” in:Problems of Mathematical Analysis [in Russian], Vol. 2 (1969), pp. 134–140.

  3. N. V. Sivitskaya and V. B. Philippov, “On the propagation of the ‘whispering gallery’ waves in a medium with a vertical interface,”Zap. Nauchn. Semin. LOMI,179, 147–151 (1989).

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  4. V. A. Fok,Problems of Diffraction and Propagation of Electromagnetic Waves [in Russian], Moscow (1970).

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Authors
  1. N. Ya. Kirpichnikova
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  2. V. B. Philippov
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 86–102.

Translated by N. Ya. Kirpichnikova.

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Kirpichnikova, N.Y., Philippov, V.B. Behavior of surface waves at transition through a junction line on the boundary of an elastic homogenous isotropic body. J Math Sci 91, 2757–2767 (1998). https://doi.org/10.1007/BF02433991

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  • DOI: https://doi.org/10.1007/BF02433991

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