Abstract: By means of the adjoints method of solving the differential equations of two-point boundary value problems⁶, the equations of motion of a boundary stress-free ceramic disk vibrator polarized in the thickness direction are solved by numerical integration. The resonance frequencies of the lower modes of radial vibration under the influence of motion in the thickness direction and the particle displacement distribution patterns are obtained for disks whose thickness-diameter ratios are less than 0.45. Correction curves for thickness effect on fundamental frequencies are given. Curves showing the effect of Poisson ratio on the relation between the first overtone-fundamental ratio and the thickness-diameter ratio are also given.
In the numberical calculations, piezoelectric properties of the ceramic disks are fully taken into consideration and no restrictions are set for the dimensions of the disks. Experimental results agree well with those obtained by calculation.