A method is given for determining the entire frequency spectra of a cylinder with cylindrical piezoelectric properties for both propagating modes and edge vibrations. Finite element modeling occurs in the radial direction so that layered profiles can be accommodated. In the vector of displacements and electric potential q(r)exp{iξz + nθ + ωt)}, quadratic polynomials are taken for q(r). Two algebraic eigenvalue problems can be deduced from this finite element formulation depending on whether the axial wave number ξ or the frequency ω acts as the eigenvalue. When real wave number ξ are assigned, an eigenvalue problem results for the natural frequency ω. When ω is assigned, then an eigenvalue problem for ξ emerges, where the values for ξ may be real (for propagating waves) or complex conjugate pairs (for edge vibrations in a semi-infinitely long cylinder). Two examples are given to illustrate the method of analysis, viz., a solid piezoelectric cylinder of PZT-4 ceramic material and a two-layer cylinder of PZT-4 covering an isotropic material.

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