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ABSTRACT
An analysis was performed on the vibration of a rectangular contoured quartz plate resonator. The surface of the resonator has different curvatures in the two in-plane directions. The analysis was based on the equation by Tiersten and Smythe, which has variable coefficients. The power series method was used. Thickness-shear and thickness-twist vibration frequencies and modes were obtained. The effects of the curvatures of the resonator surface were examined. Two types of boundary conditions were considered from which the proper size of the resonator was determined. The results are useful in the understanding of these resonators and their design.
Funding
This research was supported by a grant from the Mechanics Initiative, a COE Program of Zhejiang Provincial Government in the Department of Mechanics and Engineering Science, Ningbo University (Grant No. xklx1508), National Natural Science Foundation of China (Grant Nos. 11272161 and 11372145), the Y. K. Pao Visiting Professorship at Ningbo University, and the K. C. Wong Magana Fund through Ningbo University.