CHARACTERIZATION OF PIEZOCERAMICS

Standards on piezoelectricity described the analysis of vibrations on piezoelectric materials having simple geometrical shapes. The results are based on linear piezoelectricity and resonance modes are treated as noncoupled vibration modes. In general, due to both Poisson's ratios and piezoelectrical effects, real materials involve coupled modes. In addition, as in acoustical imaging arrays the dimension elements are nearly equal. In this case, the material characterization according to the standards no longer applies. The general constitutive equations are so complicated that an analytical resolution of these equations is impossible. Though algorithms based on the finite-element method are able to solve the steady state problem, analytical methods are often preferred because the numerical approaches do not give sufficient insight into the physical parameters that should be kept under control in the material characterization and transducer design. A new three-dimensional (3-D) approach to the piezoelectric material characterization, based on the assumption that the coordinate axes are pure mode propagation directions, is described. In this case the general equations simplify and an analytical solution can be achieved. For two geometrical shapes (rectangular and cylindrical), stress and strain tensor components and the electrical impedance of the sample are obtained. These 3-D equations show that the wave velocities and permittivity are intrinsic parameters of the medium and do not depend on either the sample geometry or the mode that is considered. It was not true for the one-dimensional (1-D) models where the wave velocities and permittivity are different for each of the modes or geometries.