Piezoelectrically forced vibrations of rectangular SC-cut quartz plates

A system of two-dimensional first-order equations for piezoelectric crystal plates with general symmetry and with electroded faces was, recently, deduced from the three-dimensional equations of linear piezoelectricity. Solutions of these equations for AT-cut plates of quartz were shown to give accurate dispersion curves without corrections, and predicted resonances agree closely with the experimental data by Koga and Fukuyo and those by Nakazawa, Horiuchi, and Ito. In the present paper, these equations are employed to study the forced vibrations of doubly rotated quartz plates. Dispersion curves for straight-crested waves propagating in the x(1) and x(3) directions of SC-cut quartz plates are computed from the three-dimensional and two-dimensional equations, respectively, and comparison shows that the agreement is very close without corrections. Resonance frequency for free vibrations and capacitance ratios for piezoelectrically forced vibrations of rectangular plates are computed and examined for various length-to-thickness or width-to-thickness ratios of plates.