Skip to main content
Log in

Elastic scattering by an obstacle in a half-space bounded by a penetrable interface

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

The solution for the problem of an elastic obstacle in the presence of a penetrable half-space excited by a dyadic elastic wave is given. Integral equations and algebraic solutions are obtained by considering the non-embedding half-space as an obstacle. Explicit results for scatterers which are small compared to all wavelengths involved are derived as well as asymptotic results for large distances from the interface.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Baños A.,Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon Oxford, New York, N.Y.) 1966.

    MATH  Google Scholar 

  2. Solakiewicz R.,Scattering by an obstacle in a half-space bounded by a penetrable interface, PhD Thesis (University of Illinois at Chicago) 1987.

    Google Scholar 

  3. Twersky V.,J. Math. Phys.,3 (1962) 83.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Twersky V.,J. Math. Phys.,8 (1967) 589.

    Article  ADS  Google Scholar 

  5. Solakiewicz R. andPhanord D.,NuovoCimento B,108 (1993) 631.

    ADS  Google Scholar 

  6. Mal A. K. andBose S. K.,Proc. Cambridge Philos. Soc,76 (1974) 589.

    Article  ADS  Google Scholar 

  7. Tan T. H.,Appl Sci. Res.,31 (1975) 364.

    Google Scholar 

  8. Kolsky H.,Stress Waves in Solids (Dover, New York, N.Y.) 1963.

    Google Scholar 

  9. Kupradze V. D.,Progress in Solid Mechanics. — III:Dynamical Problems in Elasticity (North-Holland, Amsterdam) 1963.

    Google Scholar 

  10. Brekhovskikh L.,Waves in Layered Media (Academic Press, New York, N.Y.) 1966.

    Google Scholar 

  11. Morse P. M. andFeshbach H.,Methods of Theoretical Physics (McGraw-Hill, New York, N.Y.) 1953.

    MATH  Google Scholar 

  12. Dassios G. andKiriaki K.,Q. Appl Math.,42 (1984) 225.

    MathSciNet  MATH  Google Scholar 

  13. Noether F.,Theory of Functions, edited byR. Rother,F. Ollendorf andK. Polhausen (Technology Press, Cambridge, Mass.) 1948.

    Google Scholar 

  14. Sohmerfield A.,Partial Differential Equations in Physics (Academic Press, New York, N.Y.) 1949.

    Google Scholar 

  15. Ying C. F. andTruell R.,J. Appl Phys.,27 (1956) 1086.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Einspruch N. G. andTruell R.,J. Acoust. Soc. Am.,32 (1960) 214.

    Article  MathSciNet  ADS  Google Scholar 

  17. Einspruch N. G., Witterholt E. J. andTruell R.,J. Appl Phys.,31 (1960) 806.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Pao Y-H. andMow C. C.,J. Appl Phys.,34 (1963) 493.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Varatharajulu V.,J. Math. Phys.,28 (1977) 537.

    Article  ADS  Google Scholar 

  20. Dassios G., Kiriaki K. andPolyzos D.,Int. J. Engin. Sci.,33 (1995) 269.

    Article  MathSciNet  MATH  Google Scholar 

  21. Phanord D.,Multiple scattering of elastic waves by a distribution of identical spheres, PhD Thesis (University of Illinois at Chicago) 1988.

    Google Scholar 

  22. Lucas R. andTwersky V.,J. Acoust. Soc. Am.,76 (1984) 1847.

    Article  MathSciNet  ADS  Google Scholar 

  23. Segel L.,Mathematics Applied to Continuum Mechanics (Macmillan, New York. N.Y.) 1977.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Work supported in part by National Science Foundation Grant DMS-8910594.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Phanord, D., Solakiewicz, R. Elastic scattering by an obstacle in a half-space bounded by a penetrable interface. Nuov Cim B 110, 335–353 (1995). https://doi.org/10.1007/BF02741373

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02741373

PACS

PACS

Navigation