Natural Frequency Analysis of Double-Ended Tuning Fork Piezoelectric-Quartz Resonator

• Main Authors: Pei-Ching Chang, 章蓓靜
• Other Authors: Chia-Ou Chang
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/61681707018342034595

碩士 === 國立臺灣大學 === 應用力學研究所 === 99 === The thesis mainly studied about double-ended tuning fork quartz resonator, the impact of the piezoelectric effect on a natural frequency, and the movement pattern of the relationship between an electrode arrangement and a quartz piezoelectric beam. Focusing on the analysis of the anti-phase mode, the study regards a central tuning fork as the Euler beam, and two ends of the proof masses built the warping model according to the moment caused by the anti-phase mode from the tuning fork to the proof masses; then using the constitutive law and the simulation result to make trigonometric assumption to the polarized electric potential, and obtaining the piezoelectric effect by the way of the free vibration. Assuming the coupling structure as an elastic body, and discussing the free vibration to each structure; using the Hamilton''s principle to derive the governing equation and the boundary condition for coupling the continuous relationship between the mechanics and the electrical properties. The mode shape of the vibration and the distribution patterns of the polarized electric field are used to be the design basis of exciting the specific electrode of the resonator. For understanding the impact of the process error to the resonant frequency, the study discusses the ideal cross-section of the quartz and the wet etching cross-section respectively; furthermore, the study has analyzed the impact of the dimension to the sensitivity of the resonant frequency for being the references of the process error analysis and the design of the mask; in order to improve the yield, it must get the balance between the frequency accuracy and the difficulty during the process.