Complex piezoelectric material parameters of hard PZT determined from a single disc transducer

A poled piezoelectric ceramic such as lead zirconate titanate (PZT) belongs to a C-8 crystal class, with ten independent material constants. If we consider losses, all the material parameters can be represented in complex form as all the ten material parameters also have ten loss components associated with them. Therefore, a total of 20 independent material constants are required to obtain the entire model. In this work, we present a procedure for determining the complete reduced matrix of a piezoelectric ultrasonic disc transducer using one-dimensional resonance analysis in thickness and radial modes and parametric sweep using finite element analysis to numerically calculate the impedance while comparing it with the measured impedance. The objective is to obtain the material parameters that minimize the error between the measured impedance data and the numerical impedance curve without using any optimization techniques. We can follow the standard procedure of resonance analysis for radial and thickness modes and then conduct a sensitivity analysis using parametric sweeps in COMSOL to evaluate the unknown material values. In addition, we present the transform equations in reduced matrix form to evaluate the critically sensitive parameters concerning other consistent evaluated material constant sets. To validate the procedure, we used the impedance responses of two piezoelectric discs with diameter-to-thickness ratios of 25 and 22.5. The comparison between the numerical and experimental results shows an excellent agreement for electrical impedance curves.