An analysis of frequency of a quartz crystal tuning fork by Sezawa's approximation and Winkler's foundation of the supporting Elinvar alloy wire

We developed the method to analyze the effect of the supporting wire on frequency of a quartz crystal tuning fork independent of the FEM. In order to estimate the influence of the supporting wire of tuning fork, we approximated the right half section of tuning fork to an L-shaped bar, of which the bars at both the base and the arm are in bending vibration. Furthermore, we approximated the supporting wire to elastic foundation with spring constant K. A comparison was made of frequency changes calculated by this theory with those by FEM, and the influence of spring constant K and the length of the supporting wire on frequency change calculated by this theory is discussed.