International Applied Mechanics

, Volume 50, Issue 4, pp 406–411 | Cite as

Electrically Excited Nonstationary Vibrations of Thin Circular Piezoelectric Plates

  • N. À. Shul’ga
  • L. O. Grigor’eva
  • N. O. Babkova

A numerical algorithm for analyzing the planar nonstationary axisymmetric vibrations of piezoceramic circular plates polarized across the thickness and subject to electric excitation is developed. The dynamic characteristics of a ring plate are analyzed. The dependence of the behavior of its nonstationary vibrations on the frequency of the instantaneously applied electric potential and the ratio of outer and inner radii is established


piezoelectric ring plate nonstationary electroelastic vibrations electric excitation numerical method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. A. Shul’ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies [in Russian], Naukova Dumka, Kyiv (1990).Google Scholar
  2. 2.
    M. O. Shul’ga and V. L. Karlash, Resonant Electromechanical Vibrations of Piezoelectric Plates [in Ukrainian], Naukova Dumka, Kyiv (2008).Google Scholar
  3. 3.
    N. F. Andrushko, I. K. Senchenkov, and E. V. Boichuk, “Transient waves in an inelastic disk under impulsive radial loading,” Int. Appl. Mech., 41, No. 11, 1299–1305 (2005).CrossRefADSGoogle Scholar
  4. 4.
    F. Ashida and T. R. Tauchert, “Transient response of a piezothermoelastic circular disk under axisymmetric heating,” Acta Mech., 128, 1–14 (1998).CrossRefMATHGoogle Scholar
  5. 5.
    E. Dieulesaint and D. Royer, Ondes Elastiques Dans Les Solides. Application au traitement du signal, Vol. 1, Elsevier Masson, Paris (1997).Google Scholar
  6. 6.
    H. J. Ding and W. Q. Chen, Three Dimensional Problems of Piezoelasticity, Nova Science Publ., New York (2001).Google Scholar
  7. 7.
    L. O. Grigor’eva, “Electromechanical nonstationary thickness vibrations of a piezoceramic layer,” Int. Appl. Mech., 46, No. 2, 159–164 (2010).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    V. D. Kubenko and I. V. Yanchevskii, “Vibrations of a nonclosed two-layer spherical electroelastic shell under impulsive electromechanical loading,” Int. Appl. Mech., 49, No. 3, 303–314 (2013).CrossRefADSGoogle Scholar
  9. 9.
    W. P. Mazon, “Piezoelectricity, its history and applications,” J. Acoust. Soc. Am., 70, No. 6, 1561–1566 (1981).CrossRefADSGoogle Scholar
  10. 10.
    D. Mančić, V. Dimić, and M. Radmanović, “Resonance frequencies of PZT piezoceramic disks: A numerical approach,” Facta Universitatis Series: Mechanics, Automatic Control and Robotics, 3, No. 12, 431–442 (2002).MATHGoogle Scholar
  11. 11.
    S. I. Suzuki, “Dynamic elastic response of a ring to transient pressure loading,” J. Appl. Mech., 33, No. 2, 230–235 (1966).CrossRefGoogle Scholar
  12. 12.
    M. O. Shulga and L. O. Grigoryeva, “Electromechanical nonstationary thickness vibrations of piezoceramic transformers at electric excitation,” in: Mechanical Vibrations: Types, Testing and Analysis, Nova Science Publ., New York (2011), pp. 179–204.Google Scholar
  13. 13.
    N. A. Shul’ga, V. V. Levchenko, and O. I. Makievskii, “Nonaxisymmetric electroelastic vibrations of piezoceramic ring plates with radially cut electrodes,” Int. Appl. Mech., 48, No. 4, 438–446 (2012).MathSciNetCrossRefADSGoogle Scholar
  14. 14.
    N. A. Shul’ga, V. V. Levchenko, and O. I. Makievskii, “Influence of boundary conditions on the natural frequencies of nonaxisymmetric electroelastic vibrations of piezoceramic plates,” Int. Appl. Mech., 48, No. 5, 592–601 (2012).MathSciNetCrossRefMATHADSGoogle Scholar
  15. 15.
    H. F. Tiersten, Linear Piezoelectric Plate Vibrations, Plenum Press, New York (1969).CrossRefGoogle Scholar
  16. 16.
    H. S. Tzou and R. Ye, “Piezothermoelasticity and precision control of piezoelectric systems: Theory and finite element analysis,” J. Vib. Acoust., 116, 489–495 (1994).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • N. À. Shul’ga
    • 1
    • 2
  • L. O. Grigor’eva
    • 1
    • 2
  • N. O. Babkova
    • 1
    • 2
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Kyiv Nationaly University of Construction and ArchitectureKyivUkraine

Personalised recommendations