Thickness-shear and thickness-twist vibrations of rectangular quartz crystal plates with nonuniform thickness

Lili YuanPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo, Zhejiang, China;School of Architectural Engineering, Civil Engineering and Environment, Ningbo University, Ningbo, Zhejiang, China

Rongxing WuPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo, Zhejiang, China

Jianke DuPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo, Zhejiang, ChinaCorrespondence[email protected] [email protected]

Ji WangPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo, Zhejiang, China

Jiashi YangPiezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo, Zhejiang, China;Department of Mechanical and Materials Engineering, University of Nebraska–Lincoln, Lincoln, Nebraska, USACorrespondence[email protected] [email protected]

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.

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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.

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Thickness-shear and thickness-twist vibrations of rectangular quartz crystal plates with nonuniform thickness

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Thickness-shear and thickness-twist vibrations of rectangular quartz crystal plates with nonuniform thickness

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