Skip to main content
SpringerLink
Log in

Longitudinal vibrations of a Rayleigh-Bishop rod

  • Mechanics
  • Published:
Doklady Physics Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. N. Tikhonov and A. A. Samankiĭ, Equations of Mathematical Physics (Nauka, Moscow, 1972; Pergamon Press, Oxford, 1964).

    Google Scholar 

  2. G. N. Polozhiĭ, Equations of Mathematical Physics (Vysshaya Shkola, Moscow, 1964) [in Russian].

    Google Scholar 

  3. I. Fedotov, J. Marais, and M. Shatalov, Electron. Trans. Numer. Anal. 24, 66 (2006).

    MATH  MathSciNet  Google Scholar 

  4. J. W. Strutt (Lord Rayleigh), Theory of Sound (GITTL, Moscow, 1955), Vol. 1, pp. 273–274 [in Russian].

    Google Scholar 

  5. I. A. Fedotov, A. D. Polyanin, and M. Yu. Shatalov, Dokl. Phys. 52(11), 607 (2007) [Dokl. Akad. Nauk 417 (1), 56 (2007)].

    Article  MATH  ADS  Google Scholar 

  6. J. S. Rao, Advanced Theory of Vibration (Wiley, New York, 1992), pp. 158–184.

    Google Scholar 

  7. I. Fedotov, Y. Gai, and M. Shatalov, Electron. Trans. Numer. Anal. 24, 66 (2006).

    MATH  MathSciNet  Google Scholar 

  8. A. N. Krylov, Collected Works (Akad. Nauk SSSR, Moscow, 1949), Vol. 2 [in Russian].

    Google Scholar 

  9. S. P. Timoshenko, Vibration Problems in Engineering, 3rd ed. (Mashinostroenie, Moscow, 1985; Van Nostrand, New York, 1955).

    Google Scholar 

  10. A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists (Chapman & Hall/CRC Press, Boca Raton, 2002).

    MATH  Google Scholar 

  11. L. D. Akulenko and S. V. Nesterov, High Precision Methods in Eigenvalue Problems and their Applications (Chapman & Hall/CRC Press, Boca Raton, 2004).

    Book  Google Scholar 

  12. H. Bateman and A. Erdélyi, Higher Transcendental Functions (Nauka, Moscow) [in Russian].

  13. L. J. Slater, Generalized Hypergeometric Function (Cambridge Univ. Press, Cambridge, 1966).

    Google Scholar 

  14. B. Dwork, Generalized Hypergeometric Functions (Clarendon, Oxford, 1990).

    MATH  Google Scholar 

  15. I. Fedotov, M. Shatalov, and J. N. Mwambakana, Proc. TIME-2008 Int. Conference, Buffelspoort, Tshwane Univ. Technol., 2008.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tshwane University of Technology, Pretoria, Republic of South Africa

    I. A. Fedotov, M. Yu. Shatalov & H. M. Tenkam

  2. Institute for Problems of Mechanics, Russian Academy of Sciences, Moscow, 117526, Russia

    A. D. Polyanin

  3. Department of Material Science and Manufacturing, Council for Scientific and Industrial Research (CSIR), Pretoria, Republic of South Africa

    M. Yu. Shatalov

Authors
  1. I. A. Fedotov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. D. Polyanin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Yu. Shatalov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. M. Tenkam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. D. Polyanin.

Additional information

Original Russian Text © I.A. Fedotov, A.D. Polyanin, M.Yu. Shatalov, H.M. Tenkam, 2010, published in Doklady Akademii Nauk, 2010, Vol. 435, No. 5, pp. 613–618.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fedotov, I.A., Polyanin, A.D., Shatalov, M.Y. et al. Longitudinal vibrations of a Rayleigh-Bishop rod. Dokl. Phys. 55, 609–614 (2010). https://doi.org/10.1134/S1028335810120062

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1028335810120062

Keywords

Search

Navigation