Problems of Steady Vibrations in Elasticity

  • Merab Svanadze
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 51)


In this chapter, the basic internal and external BVPs of steady vibrations in the linear theory of elasticity for quadruple porosity materials are investigated by means of the potential method and the theory of singular integral equations.


  1. 102.
    Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edn. Springer, New York (2013)CrossRefGoogle Scholar
  2. 141.
    Fosdick, R., Piccioni, M.D., Puglisi, G.: A note on uniqueness in linear elastostatics. J. Elast. 88, 79–86 (2007)MathSciNetCrossRefGoogle Scholar
  3. 155.
    Giraud, G.: Sur une classe generale d’equation a integrales principales. C. R. Acad. Sci. Paris 202, 2124–2126 (1936)zbMATHGoogle Scholar
  4. 169.
    Hsiao, G.C., Wendland, W.L.: Boundary Integral Equations. Springer, Berlin (2008)CrossRefGoogle Scholar
  5. 204.
    Knops, R.J., Payne, L.E.: Uniqueness Theorems in Linear Elasticity. Springer Tracts in Natural Philosophy, vol. 19. Springer, New York (1971)Google Scholar
  6. 205.
    Kohn, J.J., Nirenberg, L.: An algebra of pseudo-differential operators. Commun. Pure Appl. Math. 18, 269–305 (1965)MathSciNetCrossRefGoogle Scholar
  7. 219.
    Kupradze, V.D., Gegelia, T.G., Basheleishvili, M.O., Burchuladze, T.V.: Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. North-Holland, Amsterdam (1979)Google Scholar
  8. 249.
    Mikhlin, S.G.: Composition of double singular integrals (Russian). Dokl. Akad. Nauk SSSR 2(11), 3–6 (1936)zbMATHGoogle Scholar
  9. 251.
    Mikhlin, S.G.: An addition to the paper “Singular integral equations with two independent variables” (Russian). Mat. Sbornik 1(43), 953–954 (1936)Google Scholar
  10. 252.
    Mikhlin, S.G.: Multidimensional Singular Integrals and Integral Equations. Pergamon Press, Oxford (1965)zbMATHGoogle Scholar
  11. 253.
    Mikhlin, S.G., Prössdorf, S.: Singular Integral Operators. Springer, Berlin (1986)CrossRefGoogle Scholar
  12. 292.
    Russo, R., Starita, G.: Uniqueness in Linear Elastostatics. In: Hetnarski R.B. (ed.) Encyclopedia of Thermal Stresses, pp. 6311–6325. Springer, Dordrecht (2014)CrossRefGoogle Scholar
  13. 399.
    Zaman, S.I.: A comprehensive review of the boundary integral formulations of acoustic scattering problems. Journal of Scientific Research Science and Technology, Special Edition, pp. 281–310 S.Q.U. Oman (2000)Google Scholar
  14. 250.
    Mikhlin, S.G.: Singular integral equations with two independent variables (Russian). Mat. Sbornik 1(43), 535–552 (1936)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Merab Svanadze
    • 1
  1. 1.Ilia State UniversityTbilisiGeorgia

Personalised recommendations