Frequency shift calculations for quartz resonators

A technique has been developed to calculate frequency shifts for quartz resonators arising from mechanical stresses. This solution technique utilizes finite-element analysis. The solution technique is general in that any combination of mount and resonator geometries may be modeled. The frequency perturbation calculation includes movement of the mode to any position in the general vicinity of the resonator center. Experimental results for AT- and SC-cut resonators subjected to diametric force and inertial loading verify the accuracy of frequency shifts calculated using the proposed solution technique. Minimum acceleration sensitivities corresponding to optimum mode locations and mount orientations were calculated for ideal SC-cut crystal units. Simple mount imperfections were modeled to determine what affect these might have on resonator performance