Piezoelectric thin shell theoretical model and eigenfunction analysis of radially polarized ceramic cylinders

Abstract

A piezoelectric thin shell theoretical model of radially polarized ceramic cylinders is first developed. An eigenfunction approach is then used to determine the displacement, stress, electric field, and input electrical admittance of the cylinder. In the model, the effect of bending strain is included and it is assumed that the electric field varies linearly between the electrodes. The electrostatic condition is then used to express the electric field in terms of the displacement. Next, the equations of motion and the boundary conditions are derived by using Hamilton’s variational principle. They have the same form as the corresponding equations for a thin elastic shell and are solved after expressing the frequency-dependent displacement as the sum of the static displacement and a weighted sum of the eigenfunctions of the short-circuited cylinder. The eigenfunctions are determined here by using a general method and, therefore, cylinders with arbitrary boundary conditions can be analyzed. It is shown that experimental resonance frequencies and input electrical admittance of free-free cylinders are in good agreement with those computed here and that the electric field is in good agreement with results obtained by other investigators who used a numerical method to solve the equations.