An analysis of frequency of a quartz crystal tuning fork resonator by modifidy Sezawa's theory

The resonance frequency of a quartz crystal tuning fork resonator for applications in communication and electronic system has been analyzed by Sezawa with Euler-Bernoulli beam theory and modifications. To improve the accuracy in the vibration frequency and mode shape prediction, the Timoshenko beam theory is used with the resonator model and boundary conditions. The solution procedure is the same and the results are different with noticeable gap. This reminds us that the analytical solutions are to be validated with other techniques before it can be used in the resonator design and optimization. The emerging applications of tuning fork type resonators through MEMS technology demands further analytical studies with new approaches.