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On the wave transmission across the interface of two elastic half spaces with nonlocal cohesion forces

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Summary

Wave propagation across the interface of two elastic half-infinite media is examined assuming long-range action of cohesive forces. The nonlocal elastic moduli are first established by solving an auxiliary problem involving longitudinal waves in an infinite space. With constitutive equations determined, the conditions of continuity of displacements and of balance of forces at the interface of the media lead to the relations between the amplitudes of the incident, reflected and transmitted wave. The relations are illustrated by graphs.

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References

  1. Eringen, A. C.: Nonlocal polar field theories. In: Continuum Physics (Eringen, A. C., ed.)4, pp. 205–265. New York: Academic Press 1976.

    Google Scholar 

  2. Kroener, E.: Continuum mechanics and range of atomic cohesion forces. Proc. Int. Conf. Fracture1, p. 27, Soc. Fract. Mat., Sendai, 1966.

    Google Scholar 

  3. Kunin, I. A.: Elastic media with microstructure.1 (1982),2 (1983), Berlin: Springer-Verlag.

    Google Scholar 

  4. Edelen, D. G. B.: Nonlocal field theories. In: Continuum Physics (Eringen, A. C., ed.)4, pp. 76–204, New York: Academic Press 1976.

    Google Scholar 

  5. Cochran, W.: Interpretation of phonon dispersion curves. In: Lattice dynamics (Wallis, R. G., ed.), pp. 75–84. Oxford: Pergamon 1965.

    Google Scholar 

  6. Eringen, A. C.: On Rayleigh surface waves with small wave length. Lett. Appl. Eng. Sci.1, 11–17 (1973).

    Google Scholar 

  7. Nowinski, J. L.: On the nonlocal aspects of the propagation of Love waves. Int. J. Eng. Sci.22, 383–392 (1984).

    Google Scholar 

  8. Ari, N., Eringen, A. C.: Nonlocal stress field at Griffith crack. Cryst. Latt. Def. of Amorph. Mat.16, 33–38 (1983).

    Google Scholar 

  9. Eringen, A. C.: Continuum mechanics at the atomic scale. Cryst. Latt. Def.7, 109–130 (1977).

    Google Scholar 

  10. Kittel, C.: Introduction to solid state physics. New York: Wiley 1962.

    Google Scholar 

  11. Leibfried, G.: Lattice dynamics of mechanical and thermal properties of crystals (in German), Encycl. of Physics,7/1, pp. 104–324. Berlin: Springer-Verlag 1955.

    Google Scholar 

  12. Lindsay, R. B.: Mechanical radiation. New York: McGraw-Hill 1960.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mech. Engineering, University of Delaware, 19716, Newark, DE, U.S.A.

    J. L. Nowinski

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  1. J. L. Nowinski
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Nowinski, J.L. On the wave transmission across the interface of two elastic half spaces with nonlocal cohesion forces. Acta Mechanica 78, 209–218 (1989). https://doi.org/10.1007/BF01179217

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  • DOI: https://doi.org/10.1007/BF01179217

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