Analysis of axially polarized piezoelectric cylinders with arbitrary boundary conditions on flat surfaces

A method to analyze axially polarized piezoelectric ceramic cylinders with arbitrary length to radius ratio and arbitrary boundary conditions on the flat surfaces is presented. The method is based on the use of functions that individually exactly satisfy the axisymmetric equations of motion and the Gauss electrostatic conditions. The axial and radial components of displacement and the potential are expressed as weighted sums of these functions. The functions form complete sets in the radial direction and arbitrary boundary conditions can, therefore, be satisfied on the flat surfaces. On the curved surface, certain uniform boundary conditions can be exactly satisfied. The weights are easily determined by using the orthogonal property of the functions. The input electrical admittance is a function of only the average boundary conditions and is very easily determined. Several special cases and numerical results are presented for electrically and mechanically excited cylinders to illustrate the method. The series expressions for displacements, potential, and stress converge rapidly and they are in good agreement with results obtained using ATILA--a finite element program. The method can be extended to analyze hollow cylinders with arbitrary boundary conditions on all surfaces.