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Mindlin plate theory is widely used in the analysis of thickness-shear vibrations of quartz crystal resonators with analytical solutions of frequency and displacements. In the design of resonators, we always want to get accurate solutions for the determination of structural parameters. With complicated boundary conditions and geometry by taking packaging and electrodes into consideration, it will...
The theory and method have been extensively studied for the design of quartz crystal resonators, and Mindlin plate theory is widely used. As most research were aimed to solve specific problems of vibrations, there is no application program for the design. An integrated program based on Mindlin plate theory for the AT-cut quartz crystal resonators have been developed in our study, because AT-cut quartz...
High frequency vibrations of quartz crystal plates have been subjected to extensive studies for applications in the design and analysis of quartz crystal resonators functioning at the fundamental thickness-shear mode and its overtones. One important result needed in studies and product design is the exact dispersion relations of quartz crystal plates to be used for the validation of approximate theories,...
Finite element analysis is a powerful approach to the vibration analysis of complicated structures including the piezoelectric acoustic wave resonators such as the quartz crystal resonators, which usually vibrate at the thickness-hear mode with much higher frequency. The analysis has been done with the Mindlin plate equations for straight-crested wave solutions for displacements and vibration frequency,...
As demands for high frequency quartz crystal resonators rise, we are prompted to design and make overtone devices with the same material, process, and technology. Indeed, high-order overtone resonators have been widely utilized in many applications and further demands in precision products are also growing. The design of overtone resonators and further improvement of the existing ones to meet precision...
The design and analysis of quartz crystal resonators in the fundamental thickness-shear mode have been extensively studied with many methods including the simple model based on finite plates for the vibration frequency and Mindlin plate theory for couplings of the fundamental thickness-shear and spurious modes. These methods are widely used in the design process for the optimal determination of crystal...
The effectiveness of theoretical approaches based on the initial thermal field on vibrations elastic solids has been demonstrated by a series of analyses concerning the thermal behavior of crystal resonators with results in good agreement with measurements. These equations have been implemented in a finite-element method in addition to simple analytical solutions we are familiar with. Starting with...
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