The Force-Frequency Characteristics of Quartz Wafers under a Cantilever Beam Structure.

This study investigated the force-frequency characteristics of quartz wafers inside a cantilever beam frame. Firstly, the force-frequency coefficient formula of quartz wafers with fixed ends under axial force was analyzed. Firstly, the formula for the force-frequency coefficient of quartz wafers with fixed ends under axial force was analyzed.

Resonant frequency function of thickness-shear vibrations of rectangular crystal plates.

The resonant frequencies of thickness-shear vibrations of quartz crystal plates in rectangular and circular shapes are always required in the design and manufacturing of quartz crystal resonators. As the size of quartz crystal resonators shrinks, for rectangular plates we must consider effects of both length and width for the precise calculation of resonant frequency. Starting from the three-dimensional equations of wave propagation in finite crystal plates and the general expression of vibration modes, we obtained the relations between frequency and wavenumbers.