Acoustical Physics

, Volume 64, Issue 6, pp 651–658 | Cite as

Analysis of Forced Vibrations in a Functionally Gradient Cylindrical Waveguide

  • A. O. Vatul’yanEmail author
  • V. O. YurovEmail author


Wave propagation that occurs in a prestressed cylindrical waveguide with inhomogeneity along the radial coordinate under a periodic radial load concentrated in a ring-shaped region is investigated. With the use of Fourier integral transform, the problem is reduced to analyzing an operator sheaf depending on two parameters. Structural features of the dispersion set are investigated, and displacement components are determined based on the theory of residues and the analysis of an auxiliary spectral problem.


cylindrical waveguide inhomogeneity prestresses dispersion relations far fields 



This work was supported by the Russian Science Foundation (project no. 18-11-00069).


  1. 1.
    V. T. Grinchenko and V. V. Meleshko, Harmonic Vibrations and Waves in Elastic Bodies (Nauka, Moscow, 1981) [in Russian].zbMATHGoogle Scholar
  2. 2.
    I.I. Vorovich, V.A. Babeshko, Mixed Dynamic Problems in the Theory of Elasticity for Non-classical Domains (Nauka, Moscow, 1979) [in Russian].zbMATHGoogle Scholar
  3. 3.
    A. N. Guz’, F. G. Makhort, and O. I. Gushcha, Introduction to Acoustic Elasticity (Naukova dumka, Kiev, 1977) [in Russian].Google Scholar
  4. 4.
    A. N. Guz’, Elastic Waves in Bodies with Initial (Residual) Stresses (A. S. K., Kiev, 2004) [in Russian].Google Scholar
  5. 5.
    A. L. Uglov, V. I. Erofeev, and A. N. Smirnov, Acoustic Control of Equipment during its Manufacture and Operation (Nauka, Moscow, 2009) [in Russian].Google Scholar
  6. 6.
    N. E. Nikitina, Acoustoelasticity. Experience of Practical Application (TALAM, Novgorod, 2005) [in Russian].Google Scholar
  7. 7.
    V. V. Kalinchuk and I. B. Polyakova, Prikl. Mat. Mekh. 45, 384 (1981).Google Scholar
  8. 8.
    V. V. Kalinchuk and T. I. Belyankova, Surface Dynamics of Inhomogeneous Media (Fizmatlit, Moscow, 2009) [in Russian].zbMATHGoogle Scholar
  9. 9.
    M. Mazzotti, A. Marzani, I. Bartoli, and E. Viola, Int. J. Solids Struct., No. 49, 2359 (2012).Google Scholar
  10. 10.
    M. Mazzotti, A. Marzani, I. Bartoli, and E. Viola, Ultrasonics, No. 53, 1227 (2013).Google Scholar
  11. 11.
    An Jian, Yan Xiaohan, Lv Xiaoxia, and Wen Zi, Sci. Sintering, No. 49, 359 (2017).CrossRefGoogle Scholar
  12. 12.
    B. Mercer, K. K. Mandadapu, and P. Papadopoulos, Int. J. Solids Struct. 96, 162 (2016).CrossRefGoogle Scholar
  13. 13.
    A. O. Vatul’yan and A. V. Morgunova, Acoust. Phys. 61, 265 (2015).ADSCrossRefGoogle Scholar
  14. 14.
    A. O. Vatul’yan and V. O. Yurov, J. Appl. Mech. Tech. Phys. 57, 731 (2016).ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    D. Gusakov and A. Vatul’yan, Z. Angew. Math. Mech. 98, 532 (2018).CrossRefGoogle Scholar
  16. 16.
    A. O. Vatul’yan, V. V. Dudarev, and R. D. Nedin, Prestressing: Modeling and Identification (Yuzh. Fed. Univ., Rostov-on-Don, 2014) [in Russian].Google Scholar
  17. 17.
    E. Trefftz, Z. Angew. Math. Mech. 12, 160 (1933).CrossRefGoogle Scholar
  18. 18.
    R. A. Sadykov, V. I. Potapov, A. A. Ermolenko, and E. A. Trofimov, Vestn. YuUrGU, Ser. Metall. 13 (2), 85 (2013).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Southern Federal UniversityRostov-on-DonRussia

Personalised recommendations