Determination of complex coefficients of radially polarized piezoelectric ceramic cylindrical shells using thin shell theory.

A method is presented to determine the complex coefficients eT33, sE11, sE12, and d31 of piezoelectric materials. The real parts of these coefficients are determined using axially polarized thin discs in the ANSI/IEEE Standard but are determined here using radially polarized cylindrical shells. The coefficients are determined by iteratively refining them until the values of the low-frequency complex admittance, three resonance frequencies, and three bandwidths computed using a thin-shell analytical model and the coefficients are very nearly equal to measured values. The accuracy of the method is determined by using quantities computed using a finite-element model in place of measured values. Measurement errors are accounted for by using a resolution of 10 Hz to compute the critical frequencies. The differences between the coefficients input to the finite-element model and those obtained using the iteration method are the errors. It is shown that the method is sufficiently accurate to use thin radially polarized cylindrical shells to determine the properties of new materials as well as characterize those used in hydrophones or other devices.