Mass loading induced frequency shift of a thickness-shear vibrating quartz crystal plate considering size effect based on the modified couple stress theory
Mass loading induced frequency shift of a thickness-shear vibrating quartz crystal plate considering size effect based on the modified couple stress theory
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DOI：
10.1080/15376494.2020.1859656
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发表时间：
2020-12
影响因子：
2.8
通讯作者：
X. Xie;Jiemin Xie;Shan Jiang;J. Lei
中科院分区：
文献类型：
--
作者：
X. Xie;Jiemin Xie;Shan Jiang;J. Lei
摘要 根据哈密顿原理和修正耦合应力理论，建立了质量加载下尺寸相关石英晶体板厚度剪切振动的机电耦合模型。通过数值算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。石英板越薄，尺寸对频移的影响越显着，越有利于质量传感。而且，对于很薄的石英板和较大的质量比，忽略压电效应会导致较大的频移误差。但当传感器薄到一定厚度时，由于尺寸效应的主导作用，该误差会减小。
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.