Skip to main content

Problems of Steady Vibrations in Elasticity

  • Chapter
  • First Online:

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 51))

Abstract

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.

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

Buying options

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 EPUB and 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
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

References

  1. Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edn. Springer, New York (2013)

    Book  Google Scholar 

  2. Fosdick, R., Piccioni, M.D., Puglisi, G.: A note on uniqueness in linear elastostatics. J. Elast. 88, 79–86 (2007)

    Article  MathSciNet  Google Scholar 

  3. Giraud, G.: Sur une classe generale d’equation a integrales principales. C. R. Acad. Sci. Paris 202, 2124–2126 (1936)

    MATH  Google Scholar 

  4. Hsiao, G.C., Wendland, W.L.: Boundary Integral Equations. Springer, Berlin (2008)

    Book  Google Scholar 

  5. 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. Kohn, J.J., Nirenberg, L.: An algebra of pseudo-differential operators. Commun. Pure Appl. Math. 18, 269–305 (1965)

    Article  MathSciNet  Google Scholar 

  7. 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. Mikhlin, S.G.: Composition of double singular integrals (Russian). Dokl. Akad. Nauk SSSR 2(11), 3–6 (1936)

    MATH  Google Scholar 

  9. 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. Mikhlin, S.G.: Multidimensional Singular Integrals and Integral Equations. Pergamon Press, Oxford (1965)

    MATH  Google Scholar 

  11. Mikhlin, S.G., Prössdorf, S.: Singular Integral Operators. Springer, Berlin (1986)

    Book  Google Scholar 

  12. Russo, R., Starita, G.: Uniqueness in Linear Elastostatics. In: Hetnarski R.B. (ed.) Encyclopedia of Thermal Stresses, pp. 6311–6325. Springer, Dordrecht (2014)

    Chapter  Google Scholar 

  13. 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. Mikhlin, S.G.: Singular integral equations with two independent variables (Russian). Mat. Sbornik 1(43), 535–552 (1936)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Svanadze, M. (2019). Problems of Steady Vibrations in Elasticity. In: Potential Method in Mathematical Theories of Multi-Porosity Media. Interdisciplinary Applied Mathematics, vol 51. Springer, Cham. https://doi.org/10.1007/978-3-030-28022-2_6

Download citation

Publish with us

Policies and ethics