An analysis of quartz crystal resonators made from a convex piezoelectric plate of arbitrary shape

The paper addresses an analysis of the transversely varying thickness modes of a piezoelectric resonator affected by a convex anisotropic boundary surface. We show that anisotropy of the boundary surface strongly influences the eigen vibrations and capacitances. The relations to calculate the frequency spectrum, relative amplitudes of vibrations and motional capacitances are derived. A numerical simulation is provided for the crystal resonator of SBTC-cut.