IEEE 176-1987

This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section , all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields. Real materials involve mechanical and electrical dissipation. In addition, they may show strong nonlinear behavior, hysteresis effects, temporal instability (aging), and a variety of magneto-mechano-electric interactions. For example, poled ferroelectric ceramics, commonly called piezoelectric ceramics, are a class of materials of major importance in commercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearities and aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear or aging effects in ceramics, it does present the equations commonly used to determine the piezoelectric properties of poled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number of examples. It is not possible to state concisely a specific set of conditions under which the definitions and equations contained in this standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on the validity of an analysis carried out for an ideal piezoelectric material. ANSI/IEEE Std 177-1966 [5] discusses in detail the electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuit that can be used to represent these resonators in a frequency range near fundamental resonance. Section of this standard also provides discussion of the bounds imposed on the application of this standard to real materials. In brief, measurements based on this standard will be most meaningful when they are carried out on piezoelectric materials with small dissipations and negligible nonlinearities, like single-crystal dielectric solids or high-coupling-factor ceramics.