Comparative analysis of the electroelastic thickness vibrations of layers with curved boundaries

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

The three-dimensional equations of electroelasticity in Cartesian, cylindrical, and spherical coordinates are represented in Hamiltonian form with respect to the thickness coordinate. The boundary-value problem with a harmonic potential difference and zero mechanical load given on the boundaries is solved numerically. The amplitude–frequency characteristics and natural frequencies are compared. The resonant and antiresonant frequencies of the current and the dynamic electromechanical coupling coefficient are determined


piezoelectric layer sphere plate with transverse polarization electroelastic thickness vibrations amplitude–frequency characteristics resonant and antiresonant frequencies 


  1. 1.
    E. Dieulesaint and D. Royer, Elastic Waves in Solids: Applications to Signal Processing, Wiley-Interscience, New York (1981).Google Scholar
  2. 2.
    M. A. Pavlovskii, Theoretical Mechanics [in Ukrainian], Tekhnika, Kyiv (2002).Google Scholar
  3. 3.
    V. M. Sharapov, I. G. Minaev, Yu. Yu. Bondarenko, et al., Piezoelectric Transducers [in Russian], ChDTU, Cherkassy (2004).Google Scholar
  4. 4.
    M. O. Shul’ga, “Thickness elastoplastic vibrations of piezoelectric layers with curved boundaries,” Dop. NAN Ukrainy, No. 6, 59–62 (2010).Google Scholar
  5. 5.
    N. A. Shul’ga, Fundamentals of the Mechanics of Periodically Layered Media [in Russian], Naukova Dumka, Kyiv (1981).Google Scholar
  6. 6.
    N. A. Shul’ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies [in Russian], Naukova Dumka, Kyiv (1990).Google Scholar
  7. 7.
    A. Ya. Grigorenko, T. L. Efimova, and I. A. Loza, “Free vibrations of axially polarized piezoceramic hollow cylinders of finite length,” Int. Appl. Mech., 46, No. 6, 625–633 (2010).ADSCrossRefGoogle Scholar
  8. 8.
    A. Ya. Grigorenko and I. A. Loza, “Free nonaxisymmetric vibrations of radially polarized hollow piezoceramic cylinders of finite length,” Int. Appl. Mech., 46, No. 11, 1229–1237 (2010).CrossRefGoogle Scholar
  9. 9.
    W. P. Mason, “Piezoelectricity, its history and application,” J. Acoust. Soc. Am., 70, No. 6, 1561–1566 (1981).ADSCrossRefGoogle Scholar
  10. 10.
    N. A. Shul’ga, “Propagation of harmonic waves in anisotropic piezoelectric cylinders. Homogeneous piezoceramic wavequides,” Int. Appl. Mech., 38, No. 8, 933–953 (2002).CrossRefGoogle Scholar
  11. 11.
    N. A. Shul’ga, “Propagation of harmonic waves in anisotropic piezoelectric cylinders. Compound waveguides,” Int. Appl. Mech., 38, No. 12, 1440–1458 (2002).CrossRefGoogle Scholar
  12. 12.
    N. A. Shul’ga, “Theory of dynamical processes in mechanical systems and materials of regular structure,” Int. Appl. Mech., 45, No. 12, 1301–1330 (2009).CrossRefGoogle Scholar
  13. 13.
    N. A. Shul’ga, “A mixed system of equations of elasticity,” Int. Appl. Mech., 46, No. 3, 264–268 (2010).CrossRefGoogle Scholar
  14. 14.
    N. A. Shul’ga, L. O. Grigoreva, and V. F. Kornienko, “Harmonic thickness vibrations of inhomogeneous elastic layers with curved boundaries,” Int. Appl. Mech., 47, No. 1, 62–69 (2011).CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of UkraineKyivUkraine

Personalised recommendations