Dependence of frequency-temperature characteristics of quartz resonators on form, dimensions and local variations of thickness of piezoelectric crystal

An algorithm and computing program for solving a boundary-value problem are developed to determine temperature dependencies of eigenvalues and eigenfunctions of quartz resonators with rotated Y-cut piezoelectric crystals with axial symmetry and varying thickness. The possibility of determining of these dependencies is demonstrated for crystals with varying thickness and different cut directions for both harmonic and nonharmonic vibrations