International Applied Mechanics

, Volume 45, Issue 3, pp 282–289 | Cite as

Electroelastic nonstationary vibration of a piezoceramic layer

  • N. A. Shul’ga
  • L. O. Grigor’eva

A method of successive approximations is used to study the nonstationary vibration of a piezoelectric layer subject to electric and mechanical excitation and to solve associated initial–boundary-value problems. At each approximation, the method of characteristics is used. The accuracy of the method is assessed. The electrically and mechanically excited processes are compared. The dynamic electromechanical state is analyzed


method of successive approximations nonstationary vibration method of characteristics electric and mechanical loading 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. É. Babaev, Nonstationary Waves in Continua with Reflecting Surfaces [in Russian], Naukova Dumka, Kyiv (1990).Google Scholar
  2. 2.
    V. M. Bazhenov and A. F. Ulitko, “Investigation of the dynamic behavior of a piezoelectric ceramic layer during instantaneous electric loading,” Int. Appl. Mech., 11, No. 1, 16–20 (1975).Google Scholar
  3. 3.
    L. O. Grigoreva and V. M. Shul’ga, “Numerical analysis of the deformation of a piezoceramic cylinder under axisymmetric dynamic loading,” Teor. Prikl. Mekh., 42, 171–176 (2006).Google Scholar
  4. 4.
    O. Yu, Zharii and A. F. Ulitko, An Introduction to the Mechanics of Nonstationary Vibration and Waves [in Russian], Vyshcha Shkola, Kyiv (1989).Google Scholar
  5. 5.
    Yu. N. Kuliev and Kh. A. Rakhmatulin, “Longitudinal impact on a piezoceramic rod,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 5, 117–122 (1972).Google Scholar
  6. 6.
    V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity, Vol. 5 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1989).Google Scholar
  7. 7.
    G. M. Polozhii, Equations of Mathematical Physics [in Ukrainian], Radyans’ka Shkola, Kyiv (1959).Google Scholar
  8. 8.
    N. A. Shul’ga and A. M. Bolkisev, Vibration of Piezoelectric Bodies [in Russian], Naukova Dumka, Kyiv (1990).Google Scholar
  9. 9.
    N. A. Shul’ga and L. V. Borisenko, “Approximate analysis of the electroelastic vibration of a partitioned piezoceramic cylinder,” Prikl. Mekh., 26, No. 4, 120–123 (1990).MathSciNetGoogle Scholar
  10. 10.
    N. A. Shul’ga and L. O. Grigor’eva, “Propagation of two-dimensional nonstationary vibrations in an electrically excited piezoceramic prismatic body,” Int. Appl. Mech., 43, No. 11, 1258–1264 (2008).CrossRefGoogle Scholar
  11. 11.
    N. A. Shul’ga and L. O. Grigor’eva, “Solution of initial–boundary-value problems of electroelasticity revisited,” Int. Appl. Mech., 43, No. 12, 1371–1377 (2008).CrossRefGoogle Scholar
  12. 12.
    M. O. Shul’ga and V. L. Karlash, Resonant Electromechanical Vibration of Piezoelectric Plates [in Ukrainian], Naukova Dumka, Kyiv (2008).Google Scholar
  13. 13.
    M. O. Shul’ga, “On the Hamilton–Ostrogradskii principle and initial–boundary-value problems of electroelasticity,” Dop. NAN Ukrainy, No. 7, 76–81 (2008).Google Scholar
  14. 14.
    L. O. Grigor’eva, “Numerical solution to the initial–boundary-value problem of electroelasticity for a radially polarized hollow piezoceramic cylinder,” Int. Appl. Mech., 42, No. 12, 1371–1379 (2006).CrossRefGoogle Scholar
  15. 15.
    L. O. Grigor’eva, “Vibrations of a piezoceramic cylinder subject to nonstationary electric excitation,” Int. Appl. Mech., 43, No. 3, 303–308 (2007).CrossRefGoogle Scholar
  16. 16.
    V. L. Karlash, “Planar electroelastic vibrations of piezoceramic rectangular plate and half-disk,” Int. Appl. Mech., 43, No. 5, 547–553 (2007).CrossRefGoogle Scholar
  17. 17.
    V. L. Karlash, “Evolution of the planar vibrations of a rectangular piezoceramic plate as its aspect ratio is changed,” Int. Appl. Mech., 43, No. 7, 786–793 (2007).CrossRefGoogle Scholar
  18. 18.
    N. A. Shul’ga and L. O. Grigor’eva, “Method of characteristics in analysis of the propagation of electroelastic thickness oscillations in a piezoceramic layer under electric excitation,” Int. Appl. Mech., 44, No. 10, 1093–1097 (2008).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine

Personalised recommendations