Journal of Mathematical Sciences

, Volume 240, Issue 2, pp 129–140 | Cite as

Comparative Analysis of Two Methods Used for the Investigation of Harmonic Vibrations of Piezoceramic Cylinders

  • O. I. Bezverkhyi
  • L. O. Grigoryeva

We study steady-state axisymmetric vibrations of finite-length piezoceramic cylinders subjected to electric loading. A key system of equations is constructed as result of the reduction of the system of equations of electroelasticity in a cylindrical coordinate system to a system of Hamilton-type equations or by using the conditions of stationarity of the functional of Hamilton–Ostrogradskii principle. In the first case, the transition to ordinary differential equations is performed by using finite-difference expressions. In the second case, it is necessary to use spline approximations of the first-order. For the solution of the obtained boundary-value problems, we apply the method of discrete orthogonalization. The results obtained by using the indicated methods are compared. The dependence of vibrations on the frequency of loading is analyzed for a radially polarized cylinder. The resonance frequencies are determined.


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Authors and Affiliations

  • O. I. Bezverkhyi
    • 1
  • L. O. Grigoryeva
    • 1
  1. 1.Timoshenko Institute of Mechanics, Ukrainian National Academy of SciencesKievUkraine

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