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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...
In this paper, the coupled extension and thickness-twist vibrations are studied for AT-cut quartz plates under Lateral Field Excitation (LFE) with variations along the x1-direction. Mindlin’s two-dimensional equations are used for anisotropic crystal plates. Both free and electrically forced vibrations are considered. Important vibration characteristics are obtained, including dispersion relations,...
We started with the formulation of elastic bodies under initial stress and established wave velocity equation of surface acoustic waves. With four decaying indices obtained from surface acoustic wave propagation in semi-infinite isotropic elastic solid with the consideration of initial stresses, the wave velocity equation can be solved by the numerical methods. The phase velocity curves with different...
Mindlin plate theory has been playing a vital role in the analysis of high frequency vibration of quartz crystal resonators, since the coupled equations with infinite number of vibration modes have been truncated to retain essential ones with strong couplings for simplified analysis, and correction factors have been introduced to ensure exact solutions at cut-off frequencies as part of the validation...
The nonlinear longitudinal wave propagation in a rod is studied by the homotopy analysis method and obtained analytical solutions which are the same as earlier known results. We also employed the explicit and implicit finite difference methods to solve this nonlinear equation, respectively. The numerical results showed the wave form depends on many factors such as driving frequency, amplitude, nonlinear...
We formulate the first-order nonlinear Mindlin plate equations in the finite element method to study the high frequency thickness-shear vibrations of quartz crystal plates. Iterative algorisms are utilized to solve the resulted nonlinear eigensystems. High performance computational software packages are integrated into our nonlinear finite element program to speed up the extremely large scale computations...
Mindlin plate theory was first developed to provide accurate solutions for vibrations of thickness-shear mode, which has a much higher frequency than usual flexure vibrations. It has been widely used in the analysis of high frequency vibrations of quartz crystal plates, which are the core of resonators. The vibration frequency solutions obtained with Mindlin plate theory are proven much closer to...
Electrical circuit parameters such as resistance and quality factor of a quartz crystal resonator cannot be determined through vibration analysis without considering the presence of dissipation. We know that electrical parameters are strongly affected by viscosity from material damping, manufacturing, and packaging processes. The results show that the motional resistance from theoretical calculation...
A nonlinear system of two-dimensional equations for the coupled thickness-shear and flexural vibrations of electroelastic plates has been established by expanding the mechanical displacements and the electrical potential into power series in the plate thickness coordinate. By Galerkin approximation, these nonlinear partial differential equations have been first converted into two ordinary differential...
In order to understand the characteristics of the viscoelastic coating and evaluate adhesive quality, we analyzed the effect of a thin viscoelastic layer on the propagation of surface acoustic waves in an infinite plate, which can be isotropic or anisotropic. Based on an introduction of potential functions of wave propagation in the viscoelastic layer, we started from the interaction of a thin viscoelastic...
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...
Mindlin plate equations have wide applications in engineering fields with piezoelectric crystal resonators in particular due to its accurate prediction of high frequency vibrations of plates in the vicinity of thickness-shear mode. As a linear theory based on the assumption of infinitesimal deformation, its applications have been limited mainly to vibration frequency analysis. Many important properties...
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