On modeling of a thickness-shear vibrating quartz crystal plate attached with micro-beams immersed in liquid with considering couple stress effects

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• 作者：Xuan Xie ; Jiemin Xie ; Xuedong Chen and Yuantai Hu
• 刊名：ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：97
• 期：2
• 页码：190-201
• 全文大小：772K
• ISSN：1521-4001

文摘

A coupling model for a compound quartz crystal resonator (QCR) system, consisting of a QCR under the thickness-shear mode (TSM) vibrations and surface micro-beam arrays immersed in liquid, is developed using the modified couple stress theory and the Hamilton's variational principle. Couple stresses are included in both governing equations of micro-beams and the quartz crystal plate. Incorporating the boundary conditions, a set of homogeneous equations is numerically solved to get the frequency shift caused by micro-beams for different material parameters, such as Young's modulus and material characteristic length. The normalized beam deflections are plotted and discussed. Influence of couple stresses of both micro-beams and QCR together with their interaction on frequency shift is discussed in detail. The obtained results are useful in measuring geometrical and physical properties of micro-beams using plate-like acoustic wave sensors.