Analysis of Transversely Varying Thickness Modes in Trapped Energy Resonatorswith Shallow Contours

摘要

The equation for transversely varying thickness modes in doubly-rotated quartzresonators is applied in the analysis of contoured resonators with rectangular electrodes. The influence of both the contouring an the continuity conditions at the edges of the electrodes are included in the analysis. The steady state forced vibrations of contoured trapped energy resonators is treated and a lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained. Calculated results are presented for a number of trapped energy resonators with shallow contours. The treatment presented here indicates why and when the analysis for the contoured resonator which ignores the conditions at the edges of the electrodes works as well as it does. This treatment should also be used for contoured resonators with ordinary contours operating primarily in the fundamental mode when the electrodes are in a certain range of relatively small size. It is shown that this treatment may not be used for too shallow a contour because of loss of accuracy and, hence, may not be used for the flat plate. (MM).