IEEE 176-1987 pdf free.IEEE Standard on Piezoelectricity.
IEEE 176 on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectricmaterials having simple geometrical shapes.Mechanical and electrical dissipation are never introduced into thetheoretical treatment, and except for a brief discussion of nonlinear effects in Section 5.,all the results are based onlinear piezoelectricity in which the elastic，piezoelectric，and dielectric coefficients are treated as constantsindependent 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 incommercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearitiesand aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear oraging effects in ceramics , it does present the equations commonly used to determine the piezoelectric properties ofpoled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number ofexamples.
lt is not possible to state concisely a specific set of conditions under which the definitions and equations contained inthis standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on thevalidity of an analysis carried out for an ideal piezoelectric material.ANSVIEEE Std 177-1966 [5] discusses in detailthe electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuitthat can be used to represent these resonators in a frequency range near fundamental resonance.Section 6. of thisstandard 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 materialswith small dissipations and negligible nonlinearities，like single-crystal dielectric solids or high-coupling-factorceramics.
All equations and physical constants appearing in this standard are written in the International System of Units (SIunits), according to ANSIIEEE Std 268-1982 [2]. Table 1 lists many of the symbols used and, where appropriate,shows the units associated with the physical quantities designated by the symbols.IEEE 176 pdf download.