Second-Mode Tuning Forks for High Frequencies: Finite Element Analysis and Experiments

Abstract

Absmcr-Modified tuning forks are considered, with possible applications to second-mode quartz crystal tuning forks having a high effective mechanical quality factor Q, in the 100-6OO-Mlz frequency range. In order to use the quartz crystal tuning fork while maintaining a high Qe, which is inversely proportional to the square of displacements at the support, it is preferable to make a small dimensional modification of the inside arm end of the fork so that the displacements of the base end of the fork are greatly reduced. Some modifications are suggested and their effects proved for a high Q, by calculating the base displacements of tuning forks with use of the fiiite-element method. Calculated results are verified experimentally by measuring Q, of mounted tuning forks proportionately enlarged from the practical quartz tuning forks. In addition, an electrode configuration is shown that will drive the second mode and suppress the unwanted fundamental.