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

  • Vladimir B. Poruchikov

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.

Keywords

Riemann Surface Branch Point Homogeneous Solution Dynamic Problem Integration Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 7.1
    F.I. Fedorov: Theory of Elastic Waves in Crystals ( Plenum, New York 1968 )Google Scholar
  2. 7.2
    MJ.P. Musgrave: Crystal Acoustics ( Holden-Day, San Francisco 1970 )MATHGoogle Scholar
  3. 7.3
    G.I. Petrashen’: Propagation of Waves in Anisotropic Elastic Continua ( Nauka, Leningrad 1980 ) [in Russian]Google Scholar
  4. 7.4
    E.A. Kraut: Rev. Geophys. 1, 401 (1963)CrossRefADSGoogle Scholar
  5. 7.5
    S. Champin: Wave Motion 3, 343 (1981)CrossRefGoogle Scholar
  6. 7.6
    V.A. Sveklo: Dokl. Akad. Nauk SSSR 59, 5, 871 (1948) [in Russian]MATHMathSciNetGoogle Scholar
  7. 7.7
    V.A. Sveklo: J. Appl. Math. Mech. (PMM) 26, 1354 (1962)CrossRefMathSciNetGoogle Scholar
  8. 7.8
    V.A. Sveklo: Uch. Zap. Leningr. Gos. Univ., Ser. Mat. Nauk 17, 28 (1949) [in Russian]Google Scholar
  9. 7.9
    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. 7.10
    GP. Miller, MJ.P. Musgrave: Proc. Roy. Soc. A 236, 352 (1956)CrossRefMATHADSMathSciNetGoogle Scholar
  11. 7.11
    M.J.P. Musgrave: Proc. Camb. Phil. Soc. 53, 897 (1957)CrossRefMATHADSMathSciNetGoogle Scholar
  12. 7.12
    I.O. Osipov: J. Appl. Math. Mech. (PMM) 36, 874 (1972)CrossRefMATHGoogle Scholar
  13. 7.13
    V.A. Sveklo: J. Appl. Math. Mech. (PMM) 25, 1324 (1961)CrossRefMATHMathSciNetGoogle Scholar
  14. 7.14
    R. Burridge: Quart. J. Mech. Appl. Math. 24, 1, 81 (1971)CrossRefMATHMathSciNetGoogle Scholar
  15. 7.15
    V.A. Saraykin: Phys. Technol. Development Min. Resources 3, 52 (1974) [in Russian]Google Scholar
  16. 7.16
    V.A. Saraykin: Phys. Technol. Development Min. Resources 4, 65 (1974) [in Russian]Google Scholar
  17. 7.17
    C. Atkinson: Int. J. Eng. Sci. 3, 1, 77 (1965)CrossRefMATHGoogle Scholar
  18. 7.18
    J.R. Willis: Phil. Trans. Roy. Soc. London, Ser.A 274, 1240, 435 (1973)CrossRefMATHADSMathSciNetGoogle Scholar
  19. 7.19
    R. Burridge, J.R. Willis: Proc. Cambr. Phil. Soc. 66, 2, 443 (1969)CrossRefMATHADSGoogle Scholar
  20. 7.20
    V.N. Odintsev: “Some Three-Dimensional Self-Similar Elastodynamic Problems”; Ph.D. Thesis, Moscow Phys.-Techn. Institute (1973) [in Russian]Google Scholar
  21. 7.21
    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. 7.22
    V.S. Vladimirov: Generalized Functions in Mathematical Physics (Mir, Moscow 1979 )Google Scholar
  23. 7.23
    L. Hörmander: Linear Partial Differential Operators ( Springer, Berlin Gottingen Heidelberg 1963 )Google Scholar
  24. 7.24
    R. Ludwig: Comm. Pure Appl. Math. 19, 1, 49 (1966)CrossRefMATHMathSciNetGoogle Scholar
  25. 7.25
    R. Burridge: Quart. J. Mech. Appl. Math. 23, 2, 217 (1970)CrossRefMATHMathSciNetGoogle Scholar
  26. 7.26
    N.I. Muskhelishvili: Singular Integral Equations ( Nordhoff, Groningen 1953 )MATHGoogle Scholar
  27. 7.27
    B.V. Kostrov: J. Appl. Math. Mech. (PMM) 28, 1077 (1964)CrossRefMATHMathSciNetGoogle Scholar
  28. 7.28
    B.V. Kostrov: J. Appl. Math. Mech. (PMM) 28, 1, 793 (1964)CrossRefMATHMathSciNetGoogle Scholar
  29. 7.29
    V.V. Panasyuk: A Limiting Equilibrium State of Brittle Solids with Cracks (Naukova Dumka, Kiev 1968 ) [in Russian]Google Scholar
  30. 7.30
    K.B. Broberg: Arkiv Fys. 18, 2, 159 (1960)MathSciNetGoogle Scholar
  31. 7.31
    J.D. Achenbaeh, L.M. Brock: J. Elasticity 1, 1, 51 (1971)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Vladimir B. Poruchikov
    • 1
  1. 1.Institute of MechanicsMoscow State UniversityMoscowRussia

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