Two-Dimensional Analysis of Coupled Thickness-Shear and Flexural Vibrations in Rectangular AT-Cut Quartz Resonators Using a Finite-Element Method.

This paper proposes a method of two dimenslonal analysis for the thickness-flexural vibration, where the one-dimensional finite-element method (FEM) is applied to the planar equation. This approach aims at application to the analysis of the flexural spurious vibrations of strip rectangular AT-cut plate often used in practice. The feature of the proposed method is that the two-dimensional coupled vibration can be analyzed by applying twice the one-dimensional FEM. in other words, the one-dimensional FEM is applied to the eigenmode guided by the X-edge, as well as to the resonant expression derived from the boundary condition on the Z'-edge. As a result, the considered matrix is reduced greatly in size compared to the direct analysis by the two-dimensional FEM. The result of calculation for the change of the resonant frequency due to the change of the Z'-edge ratio is compared to the result of experiment, and the usefulness of the proposed method is demonstrated. It is shown also that most of the spurious vibrations depending on the Z'-edge ratio are flexural vibrations, which is a new finding. [ABSTRACT FROM AUTHOR]