An Analytical Electroacoustic Model of a Piezoelectric Composite Circular Plate

TitleAn Analytical Electroacoustic Model of a Piezoelectric Composite Circular Plate
Publication TypeJournal Article
Year of Publication2006
AuthorsPrasad, S., Q. Gallas, S. Horowitz, B. Homeijer, B. V. Sankar, L. Cattafesta, and M. Sheplak
JournalAIAA Journal
Date PublishedOCT

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 de?ection ?eld 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 veri?cation via ?nite-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.