Skip to main content
SpringerLink
Log in

Dynamic interaction of an elastic medium with a thin-walled curvilinear piezoelectric inclusion under longitudinal vibrations of a composite

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Using the method of matched asymptotic expansions, we obtain models of dynamic interaction of a thin-walled curvilinear piezoelectric inclusion of variable thickness with an elastic isotropic matrix under stationary vibrations of the composite. The elastic system is under conditions of longitudinal shear. Different cases of electric boundary conditions on the surface of the heterogeneity are considered. We propose an algorithm for the construction of boundary layer corrections for refining the behavior of displacements and stresses in the vicinity of the edge of the inclusion for its different shapes.

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

Similar content being viewed by others

References

  1. V. M. Aleksandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Coatings and Interlayers [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  2. A. E. Babaev and V. D. Kubenko, “Nonstationary aerohydroelasticity of laminated shells,” in: Mechanics of Composite Materials, Vol. 9: Dynamics of Structural Elements [in Russian], A.S.K., Kiev (1999), pp. 247–261.

    Google Scholar 

  3. M. K. Balakirev and I. A. Gilinskii, Waves in Piezoelectric Crystals [in Russian], Novosibirsk, Nauka (1982).

    Google Scholar 

  4. M. D. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, New York (1964).

    MATH  Google Scholar 

  5. I. A. Viktorov, Acoustic Surface Waves in Solids [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  6. H. S. Kit, V. F. Emets’, and Ya. I. Kunets’, “A model of elastodynamic interaction of a thin-walled inclusion with a matrix under antiplanar shear,” Mat. Met. Fiz-Mekh. Polya, 41, No. 1, 54–61 (1998); English translation: J. Math. Sci., 97, No. 1, 3810–3816 (1999).

  7. O. V. Lytvyn and V. H. Popov, “Interaction of plane harmonic waves with inclusions in the elastic space,” Fiz.-Khim. Mekh. Mater., 43, No. 3, 58–64 (2007); English translation: Mat. Sci., 43, No. 3, 361–369 (2007).

  8. A. B. Movchan and S. A. Nazarov, “Stress-strain state of a plane domain with a thin elastic inclusion of finite sizes,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 1, 75–83 (1987).

  9. A. H. Nayfeh, Perturbation Methods, John Wiley & Sons, New York (1973).

    MATH  Google Scholar 

  10. Ya. S. Pidstryhach, “Conditions of a jump of stresses and displacements on a thin-walled elastic inclusion in a continuum,” Dopov. Akad. Nauk. Ukr. RSR. Ser. A, No. 12, 29–31 (1982).

  11. Ya. S. Pidstryhach and A. P. Poddubnyak, Scattering of Acoustic Beams on Elastic Bodies of Spherical and Cylindrical Shape [in Russian], Naukova Dumka, Kiev (1986).

    Google Scholar 

  12. H. T. Sulym, Fundamentals of the Mathematical Theory of Thermoelasticity of Equilibrium of Deformable Solids with Thin Inclusions [in Russian], Doslidnyts’ko-Vydavnychyi Tsentr Shevchenko Naukove Tovarystvo, Lviv (2007).

    Google Scholar 

  13. H. T. Sulym, Ya. I. Kunets’, and R. V. Rabosh, “Asymptotic analysis of the dynamic interaction of a thin rectilinear piezoelectric inclusion with an elastic medium in longitudinal shear,” Visn. Donets. Univ., No. 1, 137–141 (2008).

    Google Scholar 

  14. V. F. Emets, Ya. I. Kunets and V. V. Matus, “Scattering of SH waves by an elastic thin-walled rigidly supported inclusion,” Arch. Appl. Mech., 73, 769–780 (2004).

    Article  MATH  Google Scholar 

  15. L. E. Fraenkel, “On the method of matched asymptotic expansions. Part I. A matching principle,” Proc. Cambridge Philos. Soc., 65, 209–231 (1969).

    Article  MathSciNet  Google Scholar 

  16. G. Johansson and A. J. Niklasson, “Approximate dynamic boundary conditions for a thin piezoelectric layer,” Int. J. Solids Struct., 40, 3477–3492 (2003).

    Article  MATH  Google Scholar 

  17. B. Zhang, A. Boström and A. J. Niklasson, “Antiplane shear waves from a piezoelectric strip actuator: exact versus effective boundary condition solutions,” Smart Mater. Struct., 13, 161–168 (2004).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    R. V. Rabosh

Authors
  1. R. V. Rabosh
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 1, pp. 101–106, January–March, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rabosh, R.V. Dynamic interaction of an elastic medium with a thin-walled curvilinear piezoelectric inclusion under longitudinal vibrations of a composite. J Math Sci 168, 625–632 (2010). https://doi.org/10.1007/s10958-010-0013-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-010-0013-z

Keywords

Search

Navigation