Generalized material model for lead magnesium niobate (PMN) and an associated electromechanical equivalent circuit

An existing one-dimensional nonlinear material model of lead magnesium niobate [J. C. Piquette and S. E. Forsythe, "A nonlinear model of lead magnesium niobate (PMN)," J Acoust. Sec. Am. 101, 289-296 (1997)] is generalized to three dimensions. The resulting theory is applied to two practical systems: the "thickness expander plate" and the "length expander bar." Linearizing the theory results in an electromechanical equivalent circuit that is applicable to predicting the first-order behavior of transducers based on either of these practical systems. The methods used are sufficiently general that the circuit is also appropriate for piezoelectric, and even for electrostatic, transducers. Preliminary experimental data that confirm the validity of the circuit are presented. Connections between the constants of the theory and those of piezoelectricity are derived, and a general expression for the coupling coefficient is obtained. Known theoretical coupling coefficients for piezoelectric and electrostatic transducers are recovered as special cases. The coupling coefficient of the PMN bar at zero prestress and zero remanent polarization is examined in some detail. For this case it is found that, to a good approximation, the bias voltage of the optimal (i.e., maximum) coupling coefficient is root 2 times the bias voltage which produces the maximum effective piezoelectric d(33) A Simple formula for estimating second harmonic distortion at zero stress and remanent polarization is given. The D field for the bar is obtained in terms of a Maclaurin series in stress. This series is asymptotic in the electric field, and is useful for estimating harmonic distortion when the stress or remanent polarization are nonzero. [S0001-4966(98)00911-4].