Mass loading induced frequency shift of a thickness-shear vibrating quartz crystal plate considering size effect based on the modified couple stress theory

An electromechanical coupling model for the thickness shear vibration of a size dependent quartz crystal plate with mass loading is established from the Hamilton's principle and the modified couple stress theory. The influence of couple stress or size effect on frequency shift and average mass sensitivity of the sensor is studied by numerical examples. The results show that couple stress or size effect can increase the frequency shift and improve the mass sensitivity as well. The thinner the quartz plate, the more significant the size effect on the frequency shift, and the more beneficial it is for mass sensing. Moreover, for very thin quartz plate and large mass ratio, ignoring piezoelectricity will cause large error of frequency shift. But this error will decrease due to the dominant role of size effect when the sensor is thin to a certain thickness.