A finite plate technique for the determination of piezoelectric material constants

An improved resonator method is presented for the determination of piezoelectric material constants. The improved method addresses a fundamental limitation of the measurement methods recommended in the current IEEE Standard on Piezoelectricity: the relations between vibrator response and material constants presented in this Standard are based upon the 1-D approximation of an essentially infinite flat plate with a uniform distribution of vibratory motion. The calculation or measurement of the effects due to the nonuniform vibrational amplitude distribution in a laterally bounded plate is a nontrivial task. The practical result is that the current IEEE 176-1987 resonator method recommendations are of limited usefulness in the determination of "intrinsic" piezoelectric material constants. This limitation can, however, readily be overcome using an improved measurement technique based on measurands unaffected by the vibrational amplitude distribution. In the improved technique, the measurands of choice are the zero-mass-loading, fundamental mode, thickness-field excitation (TE) antiresonance, or lateral-field excitation (LE) resonance frequencies. A recommended experimental procedure, using the preferred measurands, is presented.