Skip to main content
Log in

Wave processes in a hollow cylinder in an inhomogeneous prestress field

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Wave processes in an isotropic hollow cylinder located in an inhomogeneous prestress field are studied. The dispersion equation of the problem is investigated, and some features of the structure of the dispersion curves in relation to the type of prestressed state are identified. Formulas describing the behavior of the dispersion curves in the neighborhood of radial resonances are derived using the perturbation method.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. Pochhammer, “Über die Fortpflanzungsgeschwindigkeiten Kleiner Schwingungen in Einem Unbegrenzten Isotropen Kreiscylinder,” J. Reine angew. Math. 81, 324–336 (1876).

    MathSciNet  MATH  Google Scholar 

  2. C. Chree, “Longitudinal Vibrations of a Circular Bar,” J. Quart. Pure Appl. Math. 21, 287–298 (1886).

    MATH  Google Scholar 

  3. A. N. Guz’, Elastic Waves in Bodies with Initial Stresse, Vol. 2 Propagation Patterns (Naukova Dumka, Kiev, 1986) [in Russian].

    Google Scholar 

  4. A. N. Guz’, F. G. Makhort, and O. I. Gushcha, Introduction to Acoustoelasticity (Naukova Dumka, Kiev, 1977) [in Russian].

  5. A. I. Lur’e, Elastic Theory (Nauka, Moscow, 1970) [in Russian].

    Google Scholar 

  6. A. L. Uglov, V. I. Erofeev, and A. N. Smirnov, Acoustic Control of Equipment in Manufacture and Operation (Nauka, Moscow, 2009) [in Russian].

    Google Scholar 

  7. V. V. Kalinchuk and T. I. Belyankova, Dynamics of the Surface of Inhomogeneous Media (Fizmatlit, Moscow, 2009) [in Russian].

    MATH  Google Scholar 

  8. E. Trefftz, “Zur Theorie der Stabilität des Elastischen Gleichgewichts,” Z. Angew. Math. Mech. 12 (2), 160–165 (1933).

    Article  MATH  Google Scholar 

  9. Z. P. Bazant, “A Correlation Study of Formulations of Incremental Deformation and Stability of Continuous Bodies,” J. Appl. Mech. 38, 919–928 (1971).

    Article  ADS  MATH  Google Scholar 

  10. A. O. Vatul’yan and R. D. Nedin, “Models of Prestressed State and Principles of Its Identification,” in The Results of Science. South of Russia: Mathematical Forum, Vol. 8, Part 2: Research on Differential Equations, Mathematical Modeling, and Problems of Mathematical Education (South Mathematical Institute of the Vladikavkaz Scientific Center of RAS and the Government of the Republic of North Ossetia–Alania, Vladikavkaz, 2014), pp. 32–52.

    Google Scholar 

  11. I. I. Vorovich and V. A. Babeshko, Dynamic Mixed Elastic Problems for Nonclassical Regions (Nauka, Moscow, 1979) [in Russian].

    MATH  Google Scholar 

  12. V. T. Grinchenko and V. V. Meleshko, Harmonic Perturbations and Waves in Elastic Solids (Naukova Dumka, Kiev 1981) [in Russian].

  13. A. H. Nayfeh, Perturbation Methods (Wiley, New York, 1973).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. O. Vatul’yan.

Additional information

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 4, pp. 182–191, July–August, 2016.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vatul’yan, A.O., Yurov, V.O. Wave processes in a hollow cylinder in an inhomogeneous prestress field. J Appl Mech Tech Phy 57, 731–739 (2016). https://doi.org/10.1134/S0021894416040180

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021894416040180

Keywords

Navigation