Analysis of axially polarized piezoelectric ceramic cylindrical shells of finite length with internal losses.

A thin shell analytical model of axially polarized piezoelectric ceramic cylinders with internal losses is presented. The Flugge assumptions for strain-displacement relations, Hamilton's principle extended to piezoelectric shells, and the assumption that electric potential has a quadratic variation between the curved surfaces, are used to derive displacement-potential relations that are similar to equations of motion of elastic shells. A solution, with 12 coefficients, to these relations is then derived. The coefficients are complex when the shell has internal losses and are determined by using three mechanical and three electrical boundary conditions at each end--on the flat surfaces. Computed values of input electrical admittance are presented for shells with and without internal losses, and for thin shells as well as shells with wall thickness comparable to the length. They are also compared with results obtained using the finite element program--ATILA. It is shown that the analytical values of resonance frequencies, the maximum value of input electrical conductance, and the maximum and minimum values of input electrical susceptance of thin shells are in excellent agreement with finite element results. The dependence of the maxima and minima in the complex input electrical admittance on the dimensions of the shell is inferred from the numerical results.