Vibration Study of Eccentric Electrode Quartz Crystal Resonator

Quartz crystals are widely utilized in the fabrication of acoustic wave devices such as resonators, filters, and sensors due to their piezoelectric effect. Research has revealed that the electrode material, dimensions, and positioning significantly influence the performance of quartz crystal resonators. To date, only a limited number of researchers have investigated the vibrational characteristics of quartz crystal resonators with eccentric electrodes, and there remains a lack of theoretical guidance for their industrial production and manufacturing. This paper employs the variational form of the two-dimensional scalar differential equation (S-T equation) proposed by Stevens and Tiersten, utilizing the Ritz method to study the vibrational characteristics of quartz crystal resonators with eccentric electrodes. The study analyzes the impact of different electrode eccentricities and mass ratios on the vibrational modes of quartz crystal resonators, as well as the errors in resonant frequencies associated with varying electrode eccentricities, thereby providing a theoretical foundation for the actual production and processing of quartz crystal resonators.