Analysis of Shear-horizontal Vibrations of Crystal Plates for Acoustic Wave Resonators and Sensors
In this work, theoretical analysis of shear-horizontal vibrations of crystal plates under lateral electric field excitation (LFE) without and with a fluid layer is presented. A crystal plate with separated electrodes under thickness electric field excitation (TFE) in contact with a fluid layer is also analyzed.
We have started with analyzing the coupled face-shear (FS) and thickness-twist (TT) motions of piezoelectric plates with lateral electric fields, using the Mindlin's first-order theory of piezoelectric plates. Solutions for propagating waves, and for free and electrically-forced vibrations are obtained, leading to basic vibration characteristics for resonator applications including dispersion relations, frequency spectra, and motional capacitance. Numerical results are presented for AT-cut quartz plates.
We have then studied the coupled face-shear (FS) and thickness-twist (TT) motions of a piezoelectric plate with mass layers on the central parts of the plate surfaces, driven by a lateral electric field. An analytical solution is obtained. Numerical results are presented for an AT-cut quartz plate, including the motional capacitance of the plate as a resonator and vibration modes trapped under the mass layers in the central portion of the plate. The relationship between the dimensions of the mass layers and the number of trapped modes is examined.
We have studied the thickness-shear vibration of a rotated Y-cut quartz crystal plate whose one surface is in contact with a fluid layer. In this study, two configurations are considered. For the first configuration, we have analyzed the plate vibrations driven by a lateral electric field, using both the theory of piezoelectricity and the theory of Newtonian fluids. The solutions for both free and forced vibrations are obtained. Approximate expressions for the frequency shifts in the crystal plate due to the fluid are presented. The admittance of the structure is also calculated. The results illustrate the impacts of the thickness, the density and the viscosity of the fluid layer on the frequency shifts in the plate. In the second configuration, the fluid is under an electrode separated from the crystal plate and the driving electric field is in the plate thickness direction. This configuration qualitatively describes the effect of the liquid permittivity on the frequency shifts in a real LFE liquid sensor.
Finally, I studied the propagation of shear-horizontal waves in a piezoelectric plate in contact with a fluid layer as an acoustic wave sensor for measuring fluid viscosity or density. Mindlin's first-order theory of piezoelectric plates and the theory of Newtonian fluids are used. Two kinds of fluid layers are considered. One is with finite thickness, and the other is semi-infinite. Approximate dispersion relations for long face-shear and thickness-twist waves are given analytically. In the first one, numerical results only show the effects of the fluid on wave characteristics. In the other, numerical results showing the effects of the fluid and the piezoelectric coupling in the plate on wave characteristics are presented.