An Analytical Electroacoustic Model of a Piezoelectric Composite Circular Plate

Prasad, S., Gallas, Q., Horowitz, S., Homeijer, B., Sankar, B.V., Cattafesta, L., and Sheplak, M., "An Analytical Electroacoustic Model of a Piezoelectric Composite Circular Plate," AIAA Journal, Vol. 44, No. 10, pp. 2311-2318, October 2006. (Abstract)

Abstract: This paper presents an analytical two-port, lumped-element model of a piezoelectric composite circular plate. In particular, the individual components of a piezoelectric unimorph transducer are modeled as lumped elements of an equivalent electrical circuit using conjugate power variables. The transverse static deflection field as a function of pressure and voltage loading is determined to synthesize the two-port dynamic model. Classical laminated plate theory is used to derive the equations of equilibrium for clamped circular laminated plates containing one or more piezoelectric layers. A closed-form solution is obtained for a unimorph device in which the diameter of the piezoelectric layer is less than that of the shim. Methods to estimate the model parameters are discussed, and model verification via finite-element analyses and experiments is presented. The results indicate that the resulting lumped- element model provides a reasonable prediction (within 3%) of the measured response to voltage loading and the natural frequency, thus enabling design optimization of unimorph piezoelectric transducers.