Techniques to determine the complex material constants of spherical and cylindrical ring resonators

Techniques to determine the dielectric, mechanical and piezoelectric losses for radial poled spherical, hemispherical, and thickness poled ring resonators were presented. The impedance equations of these resonators were derived from the theory of thin shells as discussed by Berlincourt, Curran and Jaffe. These have been generalized to include loss by making the material constants complex. Equations relating the complex frequency constants and complex material constants were also presented. The effect of measurement noise on results was examined by adding white noise on generated spectra. Analyzed material constants were found to be within 1 percent of the material constants used to generate the spectra. Applying a nonlinear regression technique was found to further reduce error in the determined constants. The radial poled cylinder was also discussed and methods to determine the complex material constants of this resonator were presented. The use of complex material constants with samples of these geometries was further demonstrated in the analysis of several ceramic PZT resonators