Extensional, thickness-stretch and symmetric thickness-shear vibrations of piezoelectric ceramic disks

A set of two-dimensional second-order approximate equations for extensional, thickness-stretch and symmetric thickness-shear vibrations of piezoelectric ceramic plates with electroded faces is extracted from the infinite system of 2-D equations deduced in a previous paper by Lee, Yu, and Lin. The new truncation procedure developed in a recent paper by Lee and Edwards is employed for it improves the accuracy of calculated dispersion curves. Closed form solutions are obtained for free vibrations of circular disks of barium titanate. Dispersion curves calculated from the present approximate 2-D equations are compared with those from the three-dimensional equations, and the predicted resonance frequencies are compared with the experimental data by Shaw. Both comparisons show good agreement without any corrections. The frequencies of the edge modes calculated from the present 2-D equations are very close to the experimental data. Furthermore, mode shapes at various frequencies are calculated in order to identify the frequency segments of the spectrum at which one of the coupled modes, i.e., the radial extension (R), edge mode (Eg), thickness-stretch (TSt), and symmetric thickness-shear (s.TSh), is predominant