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Slow thickness shear vibrations in AT-cut quartz plates driven by a lateral electric field produced by surface electrodes are analyzed theoretically. Mindlin's first-order theory of piezoelectric plates is used. Through an electrically forced vibration analysis, the motional capacitance and mode shapes near resonances are obtained. The effects of the electrode gap, the electrode/plate mass ratio R...
In the design and optimization of quartz crystal resonators, the finite element method has been adopted for the analysis of quartz crystal plates with complications for the vibration frequency and mode shapes. Further extension of such analysis can be made by using complex solutions to extract the electrical parameters of quartz crystal resonators because it is a typical electronic component in circuit...
The thickness-shear vibrations of a quartz crystal plate serve as the functioning mode of a resonator with strong couplings to many other modes of vibrations, which can affect the frequency and mode shape, consequently the resonator properties. For applications, it is always desired to have pure thickness-shear vibrations that only exist in an infinite plate. With the three-dimensional equations of...
Quartz crystal resonators of circular type are widely used for frequency control and detection functions with the quartz crystal plate vibrating at the thickness-shear mode. Naturally, vibrations of circular quartz crystal plates are of great interests in the design and optimization of resonators. We have derived the Mindlin plate equations for the thickness-shear vibrations of circular plates in...
Thickness-shear vibrations of a plate is one of the most widely used functioning modes of quartz crystal resonators. For an analysis of vibrations, the Mindlin and Lee plate theories based on the displacement expansion of the thickness coordinate have been used as the linear theories. However, due to lacking of available method and complexity of the problem, the nonlinear thickness-shear vibrations...
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