The nonlinear electromechanical behavior of cantilevered piezoelectric ceramic bimorph, unimorph, and reduced and internally biased oxide wafer actuators is studied in a wide electric field and frequency range. It is found that under quasistatic condition, linear relationships between actuator tip displacement-electric field, and blocking force-electric field are only valid under weak field driving. With increasing the driving field, electromechanical nonlinearity begins to contribute significantly to the actuator performance because of ferroelectric hysteresis behavior associated with piezoelectric lead zirconate titanate (PZT)-type ceramic materials. The bending resonance frequencies of all these actuators vary with the magnitude of the electric field. The decrease of resonance frequency with electric field is explained by the increase of elastic compliance of PZT ceramic due to elastic nonlinearity. Mechanical quality factors of the actuators also depend on the magnitude of electric field strength. No significant temperature increase is observed when actuators are driven near resonance frequency under high electric field.

We have analyzed the performance of Rainbow (reduced and internally biased oxide wafer) actuators by assuming that the key difference between these devices and unimorph actuators is the presence of internal stress that alters the extrinsic (domain switching) contribution to electromechanical response, and thus, the effective d 31 coefficient of the piezoelectric layer. Based on this assumption, we calculated the d 31 coefficient as a function of device geometry and electric field and found that the coefficients ranged from approximately ؊300 to ؊600 pm/V. The highest d 31 value was obtained for a Rainbow actuator that was fabricated by reducing 1/3 of the piezoelectric layer; other studies indicated that this device possessed the highest tensile stress in the surface region of the piezoelectric. We observed that geometric effects on calculated d 31 coefficients were as significant as voltage effects. The analytical approach utilized also permitted estimation of the relative contributions of mechanical and stress effects to the performance of these devices, which were determined to be dependent on field and geometry. Although the estimated d 31 coefficient for certain geometries is twice the typical low field value, it must be remembered that this value represents an "average" value for the entire piezoelectric layer, which is under a stress gradient; i.e., the lower region of the piezoelectric is in lateral compression, while the upper region is in lateral tension. This suggests that the true electromechanical coefficients of the lead zirconate titanate composition utilized in these devices would display an even broader range of d 31 values, if d 31 was characterized as a function of uniform lateral stress.