Date of this Version
Huijing He, et al. "Scalar Differential Equation for Slowly-Varying Thickness-Shear Modes in AT-Cut Quartz Resonators with Surface Impedance for Acoustic Wave Sensor Application" IEEE Sensors Journal Vol. 13 Iss. 11 (2013) p. 4349 - 4355
For time-harmonic motions, we generalize a 2-D scalar differential equation derived previously by Tiersten for slowly-varying thickness-shear vibrations of AT-cut quartz resonators. The purpose of the generalization is to include the effects of surface acoustic impedance from, e.g., mass layers or ﬂuids for sensor applications. In addition to the variation of ﬁelds along the plate thickness, which is considered in the usual 1-D acoustic wave sensor models, the equation obtained also describes in-plane variations of the ﬁelds, and therefore can be used to study the vibrations of ﬁnite plate sensors with edge effects. The equation is compared with the theory of piezoelectricity in the special cases of acoustic waves and pure thickness vibrations in unbounded plates. An example of a ﬁnite rectangular plate is also given.