Mechanical & Materials Engineering, Department of
Date of this Version
6-24-2016
Citation
2018 J. Shi, et al.
Abstract
We investigated thickness-shear vibrations of a contoured, AT-cut quartz resonator with a pair of electrodes displaced from the resonator centre. The scalar differential equations by Stevens and Tiersten for thickness-shear vibrations of electroded and unelectroded quartz plates were employed. Based on the variational formulation of the scalar differential equations established in a previous paper and the variation-based Ritz method with trigonometric functions as basis functions, free vibration resonance frequencies and trapped thickness-shear modes were obtained. The effects of the electrode off centre on resonance frequencies and mode shapes were examined. When the electrode off centre is about one hundredth of the electrode length, the relative frequency shift is of the order of one part per million, significant in certain resonator design and applications. The electrode off centre also causes the loss of symmetry of modes, which has an adverse effect on resonator frequency stability under a normal acceleration.
Included in
Mechanics of Materials Commons, Nanoscience and Nanotechnology Commons, Other Engineering Science and Materials Commons, Other Mechanical Engineering Commons
Comments
International Journal of Acoustics and Vibration, Vol. 23, No. 4, 2018 (pp. 423-431) https://doi.org/10.20855/ijav.2018.23.41087