Effect of Tilted Edges on Coupled Vibrations of Doubly Rotated Quartz Plates

Abstract

We numerically analyze the two-dimensional (2-D) coupled vibrations of a doubly rotated quartz plate with tilted edges. An efficient technique that uses a combination of 1-D and 2-D finite element methods is developed to solve coupled vibrations in the Y'-Z' cross section of a parallelogram shape. When the orientation of a quartz plate is described using the IEEE notation, as (YXwlt)φ/θ/ψ, the third rotation ψ about the plate normal is selected such that the Z'-width faces are parallel to the particle motion of a slow-shear wave propagating in the Y'-thickness direction. For SC-cut plates operating in the fundamental slow thickness-shear mode, we evaluate the effect of tilted edges on the frequency spectra and the first frequency-temperature coefficients, and verify the strong decoupling effect on the thickness-shear and face-shear modes. The optimal inclination angle of tilted edges for SC and FC cuts is appropriately defined as the equiphase plane of the main displacement of the face-shear traveling wave.