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Scalar Differential Equation For Slowly-Varying Thickness-Shear Modes In At-Cut Quartz Resonators With Surface Impedance For Acoustic Wave Sensor Application, Huijing He, Jiashi Yang, John A. Kosinski
Scalar Differential Equation For Slowly-Varying Thickness-Shear Modes In At-Cut Quartz Resonators With Surface Impedance For Acoustic Wave Sensor Application, Huijing He, Jiashi Yang, John A. Kosinski
Department of Mechanical and Materials Engineering: Faculty Publications
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 …
Effects Of Mode Coupling On The Admittance Of An At-Cut Quartz Thickness-Shear Resonator, Huijing He, Jiashi Yang, Wei-Ping Zhang, Ji Wang
Effects Of Mode Coupling On The Admittance Of An At-Cut Quartz Thickness-Shear Resonator, Huijing He, Jiashi Yang, Wei-Ping Zhang, Ji Wang
Department of Mechanical and Materials Engineering: Faculty Publications
We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin’s two-dimensional equations for piezoelectric plates are employed. Electrically forced vibration solutions are obtained for three cases: pure thickness-shear mode alone; two coupled modes of thickness shear and flexure; and three coupled modes of thickness shear, flexure, and face shear. Admittance is calculated and its dependence on the driving frequency and the length/thickness ratio of the resonator is examined. Results show that near the thickness-shear resonance, admittance assumes maxima, and that for certain values of the length/thickness ratio, …