Skip to main content

Homogeneous Solutions to Dynamic Problems for Anisotropic Elastic Media (Willis’ Method)

  • Chapter
Methods of the Classical Theory of Elastodynamics
  • 167 Accesses

Abstract

In recent years, non-stationary dynamic problems involving anisotropic elastic bodies have attracted much attention from researchers because a number of important applied problems need be solved.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F.I. Fedorov: Theory of Elastic Waves in Crystals ( Plenum, New York 1968 )

    Google Scholar 

  2. MJ.P. Musgrave: Crystal Acoustics ( Holden-Day, San Francisco 1970 )

    MATH  Google Scholar 

  3. G.I. Petrashen’: Propagation of Waves in Anisotropic Elastic Continua ( Nauka, Leningrad 1980 ) [in Russian]

    Google Scholar 

  4. E.A. Kraut: Rev. Geophys. 1, 401 (1963)

    Article  ADS  Google Scholar 

  5. S. Champin: Wave Motion 3, 343 (1981)

    Article  Google Scholar 

  6. V.A. Sveklo: Dokl. Akad. Nauk SSSR 59, 5, 871 (1948) [in Russian]

    MATH  MathSciNet  Google Scholar 

  7. V.A. Sveklo: J. Appl. Math. Mech. (PMM) 26, 1354 (1962)

    Article  MathSciNet  Google Scholar 

  8. V.A. Sveklo: Uch. Zap. Leningr. Gos. Univ., Ser. Mat. Nauk 17, 28 (1949) [in Russian]

    Google Scholar 

  9. I.O. Osipov: “On a Plane-Strain Problem with a Point Source Inside an Anisotropic Solid”, in Propagation of Elastic and Elastic/Plastic Waves ( FAN, Tashkent 1969 ) [in Russian]

    Google Scholar 

  10. GP. Miller, MJ.P. Musgrave: Proc. Roy. Soc. A 236, 352 (1956)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. M.J.P. Musgrave: Proc. Camb. Phil. Soc. 53, 897 (1957)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. I.O. Osipov: J. Appl. Math. Mech. (PMM) 36, 874 (1972)

    Article  MATH  Google Scholar 

  13. V.A. Sveklo: J. Appl. Math. Mech. (PMM) 25, 1324 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  14. R. Burridge: Quart. J. Mech. Appl. Math. 24, 1, 81 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  15. V.A. Saraykin: Phys. Technol. Development Min. Resources 3, 52 (1974) [in Russian]

    Google Scholar 

  16. V.A. Saraykin: Phys. Technol. Development Min. Resources 4, 65 (1974) [in Russian]

    Google Scholar 

  17. C. Atkinson: Int. J. Eng. Sci. 3, 1, 77 (1965)

    Article  MATH  Google Scholar 

  18. J.R. Willis: Phil. Trans. Roy. Soc. London, Ser.A 274, 1240, 435 (1973)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. R. Burridge, J.R. Willis: Proc. Cambr. Phil. Soc. 66, 2, 443 (1969)

    Article  MATH  ADS  Google Scholar 

  20. V.N. Odintsev: “Some Three-Dimensional Self-Similar Elastodynamic Problems”; Ph.D. Thesis, Moscow Phys.-Techn. Institute (1973) [in Russian]

    Google Scholar 

  21. V.I. Osaulenko: “Mixed Elastodynamic Problems for Domains with Circular Line Separating Boundary Conditions and Geophysical Applications of These Problems”; PhD. Thesis, Moscow Institute of Physics of the Earth (1982) [in Russian]

    Google Scholar 

  22. V.S. Vladimirov: Generalized Functions in Mathematical Physics (Mir, Moscow 1979 )

    Google Scholar 

  23. L. Hörmander: Linear Partial Differential Operators ( Springer, Berlin Gottingen Heidelberg 1963 )

    Google Scholar 

  24. R. Ludwig: Comm. Pure Appl. Math. 19, 1, 49 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  25. R. Burridge: Quart. J. Mech. Appl. Math. 23, 2, 217 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  26. N.I. Muskhelishvili: Singular Integral Equations ( Nordhoff, Groningen 1953 )

    MATH  Google Scholar 

  27. B.V. Kostrov: J. Appl. Math. Mech. (PMM) 28, 1077 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  28. B.V. Kostrov: J. Appl. Math. Mech. (PMM) 28, 1, 793 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  29. V.V. Panasyuk: A Limiting Equilibrium State of Brittle Solids with Cracks (Naukova Dumka, Kiev 1968 ) [in Russian]

    Google Scholar 

  30. K.B. Broberg: Arkiv Fys. 18, 2, 159 (1960)

    MathSciNet  Google Scholar 

  31. J.D. Achenbaeh, L.M. Brock: J. Elasticity 1, 1, 51 (1971)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Poruchikov, V.B. (1993). Homogeneous Solutions to Dynamic Problems for Anisotropic Elastic Media (Willis’ Method). In: Methods of the Classical Theory of Elastodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77099-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-77099-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77101-9

  • Online ISBN: 978-3-642-77099-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics