Index of content:
Volume 110, Issue 2, August 2001
- TRANSDUCTION 
110(2001); http://dx.doi.org/10.1121/1.1387090View Description Hide Description
An eight-port impedance matrix and an equivalent circuit are presented for the analysis of an asymmetric triple-layered piezoelectric bimorph with separate electrical ports. The separate electric ports for the top and bottom piezoelectric layers operate independently of each other: they generate and/or sense the coupled extensional and flexural motions. Taking into account shear and rotatory inertia, the eight-port impedance model is first obtained for the bimorph. The electromechanical behavior of the piezoelectric layers, and the mechanical motions of the bimorph, are separately represented by equivalent circuits with common ports. Connecting the circuits through the common ports then leads to the overall equivalent circuit. It is demonstrated that the resonance/antiresonance frequencies and the sensor-to-actuator signal of the cantilevered bimorph for various length-to-thickness ratios can be effectively calculated by the application of the electrical networktheory to the equivalent circuit. It is also shown that the electric circuit conditions on the piezoelectric layers can alter the resonance frequencies of the bimorph without changing the mechanical conditions. All the results by the present method are in excellent agreement with those by three-dimensional finite-element methods.
110(2001); http://dx.doi.org/10.1121/1.1381537View Description Hide Description
The problem of determining the drive waveform that produces a desired output from a hysteretic, saturating material is considered both theoretically and experimentally. The specific problem of interest is the production of a high-amplitude, but monofrequency, sinusoidal polarization response. (The techniques presented could also be used to control other physical variables, such as the strain, if desired.) Two sample materials were considered, one of which is characterized by relatively low hysteresis and tested using mechanical prestresses of 20.7 MPa (3 kpsi) and 41.4 MPa (6 kpsi), and the other of which is characterized by relatively high hysteresis and tested without a prestress. Both samples were fabricated from the electrostrictive materialleadmagnesiumniobate (PMN), although a magnetostrictive material (such as Terfenol-D) could have been tested instead. The samples were subjected to a bias voltage and prestress in order to simulate conditions that might arise in a full transducer. By analytically inverting a theory of hysteresis [J. C. Piquette and S. E. Forsythe, J. Acoust. Soc. Am. 106, 3317–3327 (1999) and J. Acoust Soc. Am. 106, 3328–3334 (1999)], the required (predistorted) drive waveform was determined. Both semi-major and minor hysteresis loops, in both polarization and strain, were measured and the parameters of the theory determined by least-squares fitting. The measurements were obtained under quasi-static conditions, with drive frequencies at or below 10 Hz. The observed fits of theory to data are of high quality. The theory was then inverted analytically to determine the drive required to produce the desired monofrequency polarization response, having a peak polarization value approximately equal to that achieved using a biased sinusoid of AC amplitude equal to the bias. The total harmonic distortion (THD) in the output polarization resulting from the inverting drive, computed using 10 harmonics, was experimentally observed to be about an order of magnitude less than that resulting from a biased sinusoid in all cases. It is shown that the hysteresis loop arising when using the distortion-reducing drive is of smaller area than that obtained when driving with a sinusoid to achieve the same polarization amplitude. Thus, the distortion-reducing drive results in a smaller loss per cycle than is obtained with a sinusoidal drive.