Moment method formulation for piezoceramic plate vibrations

Presented herein is a numerical algorithm based on the method of moments that has been used recently in structural electroelastic elements [e.g., M. C. Dökmeci and G. A. Altay, Z. angew. Math. Mech. 77, 1–17 (1997) and references therein] in order to predict the dynamic response of a piezoceramic plate. The piezoceramic plate of uniform thickness is coated completely with very thin perfectly conducting electrodes on and under an electric potential applied to its faces. In the first part of the paper, the two‐dimensional equations for the piezoceramic plate are derived in both variational and differential forms by use of the differential variational principle [M. C. Dökmeci and G. A. Altay, Int. J. Eng. Sci. 34(7), 769–782 (1996)] together with a series expansion of the field variables. In the second part, the method of moments [M. C. Dökmeci, Proceedings of the 1992 Ultrasonics Symposium (IEEE, New York, 1992), pp. 1025–1028] is described for the dynamic response. The significant mechanical and electrical effects are all taken into account. The equations derived accommodate all the types of motions as well as coupled motions of the piezoceramic plate. In the third part, attention is focused on certain cases involving special geometry, motions, and polarization directions of the piezoceramic plate. [Work supported in part by TÜBA.]