International Applied Mechanics

, Volume 46, Issue 6, pp 625–633 | Cite as

Free vibrations of axially polarized piezoceramic hollow cylinders of finite length

  • A. Ya. Grigorenko
  • T. L. Efimova
  • I. A. Loza

The problem of the free axisymmetric vibrations of longitudinally polarized piezoceramic hollow cylinders is solved by a numerical analytic method. The spline-collocation method with respect to the longitudinal coordinate is used to reduce the original problem of electroelasticity to an eigenvalue boundary-value problem for ordinary differential equations with respect to the radial coordinate. This problem is solved by the stable discrete-orthogonalization and incremental search methods. Numerical results are presented and the natural frequencies of the cylinders are analyzed for a wide range of their geometric characteristics


free vibrations hollow piezoceramic cylinder spline-approximation boundary conditions 


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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • A. Ya. Grigorenko
    • 1
  • T. L. Efimova
    • 1
  • I. A. Loza
    • 2
  1. 1.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of UkraineKyivUkraine
  2. 2.National University of TransportKyivUkraine

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