Analysis of thickness-shear and thickness-twist modes of AT-cut quartz acoustic wave resonator and filter

The thickness-shear （TS） and thickness-twist （TT） vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural variations in one of the two in-plane directions of the plates only. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded AT-cut quartz plates are used, resulting in free vibration resonant frequencies and mode shapes for both fundamental and overtone fam- ilies of modes. The trapped modes with vibrations, mainly confined in the electroded areas, are found to exist in both the resonator and the filter structures. The numerical results for the trapped modes are presented for different aspect ratios of electrodes and material properties, providing a reference to the design and optimization of quartz acous- tic wave resonators and filters.