Abstract

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.

摘要

根据Hamilton原理和修正耦合应力理论，建立了具有质量载荷的尺寸相关石英晶体板的厚度剪切振动的机电耦合模型。通过数值实例研究了耦合应力或尺寸效应对传感器频移和平均质量灵敏度的影响。结果表明，耦合应力或尺寸效应可以增加频移并提高质量灵敏度。石英片越薄，尺寸对频移的影响越显着，对质量传感越有利。此外，对于非常薄的石英片和大的质量比，忽略压电性会导致较大的频移误差。