A NEW 2-DIMENSIONAL THEORY FOR VIBRATIONS OF PIEZOELECTRIC CRYSTAL PLATES WITH ELECTRODED FACES

A system of two-dimensional (2-D) governing equations for piezoelectri c plates with general crystal symmetry and with electroded faces is de duced from the three-dimensional (3-D) equations of linear piezoelectr icity by expansion in series of trigonometric functions of thickness c oordinate. The essential difference of the present derivation from the earlier studies by trigonometrical series expansion is that the antis ymmetric in-plane displacements induced by gradients of the bending de flection (the zero-order component of transverse displacement) are exp ressed by the linear functions of the thickness coordinate, and the re st of displacements are expanded in cosine series of the thickness coo rdinate. For the electric potential, a sine-series expansion is used f or it is well suited for satisfying the electrical conditions at the f aces covered with conductive electrodes. A system of approximate first -order equations is extracted from the infinite system of 2-D equation s. Dispersion curves for thickness shear, flexure, and face-shear mode s varying along x(1) and those for thickness twist and face shear vary ing along x(3) for AT-cut quartz plates are calculated from the presen t 2-D equations as well as from the 3-D equations, and comparison show s that the agreement is very close without introducing any corrections . Predicted frequency spectra by the present equations are shown to ag ree closely with the experimental data by Koga and Fukuyo [J. Inst. El ec. Comm. Engrs. of Japan 36, 59 (1953)] and those by Nakazawa, Horiuc hi, and Ito [Proceedings of 1990 IEEE Ultrasonics Symposium (IEEE, New York, 1990)]. (C) 1998 American Institute of Physics. [S0021-8979(98) 03803-1].