Finite element method has successfully applied to analyzing the axisymmetric vibrations of piezoelectric circular rod, in which the electric field is assumed to be constant. When the distance between the electrodes becomes longer so that the longitudinal and flexural vibrations are to be excited, the assumption is no longer valid. In the present paper, two types of FEM model to cope with the situation are proposed. In the first model, nodal potentials of an element are taken into account to express the arbitrary distribution of the electric field. The second model is a thin rod assumption, the electric displacement is taken to be constant. The formulation and computer programs are developed based on these two models. The natural frequencies, the corresponding modes, potential distributions and input admittance at the electrical terminales are calculated. The calculated results of input admittance are compared with the measured ones and the analytical solution. It is found that the first FEM model where the electric fields are unconstrained is capable to simulate the vibrators of any length/diameter ratio as expected, while the second model can be applied to a slender vibrator of the length/diameter of two for its lowest mode.
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