Force Frequency Effect in Square Quartz Crystals

In this investigation, the force-frequency effect in a square at-cut quartz resonator is studied. based on the force-frequency effect, by insertion of diametrical forces, the natural frequency of thickness shear vibration mode in at-cut quartz resonators is changed. this criterion is of importance in designing quartz resonators and force sensors. in this paper, the frequency change of a square at-cut quartz crystal subjected to a pair of opposing forces on different points of its edge is studied experimentally. also, the force-frequency effect in the square crystal is modeled by a previously developed mathematical-finite element model. the accuracy of the model is verified by the experimental results. then, the model is applied for evaluating the force-frequency effect in the at-cut crystal, and the frequency shifts in different loading configurations are obtained. the new loading configurations are produced by moving the loading points along the edges, and by rotating the edges of the crystal around its thickness axis. also, the distributed loading tests are performed on the crystal. based on this, the loading configurations with maximum and minimum frequency shifts are obtained. moreover, the design of quartz crystal force sensors having high sensitivity and also the crystal oscillator with high-frequency stability are discussed.