Method for obtaining the full set of linear electric, mechanical, and electromechanical coefficients and all related losses of a piezoelectric ceramic

A method based on the use of four piezoelectric resonances for three sample geometries is presented that allows one to obtain all the dielectric permittivities, compliances, and piezoelectric coefficients of a piezoelectric ceramic in complex form and, therefore, all related losses. Piezoelectric losses are responsible for heat generation and hysteresis in actuators. The method is applied to a Navy type II PZT-based piezoelectric ceramic (PZT = lead zirconate titanate), for which the full set of linear electric, mechanical, and electromechanical coefficients is given in complex form. Full sets of coefficients for the available piezoceramics are required for exploiting all the possibilities of finite element analysis, both in fundamental research (mechanisms of degradation) and in development (element design). This numerical technique is necessary to explore arbitrary shapes provided by solid free-form-fabrication technologies.