The shear mode film bulk acoustic wave resonators (FBARs) have been developed rapidly in recent years due to the increased interest in biosensors. In this article, the mode coupling effects that are unavoidable in real devices are theoretically analyzed and discussed. Mindlin’s approximation method of expanding the displacement fields with power series along the plate thickness direction is employed, and a system of 2-D plate equations is obtained. The accuracy of the plate theory is validated through the comparison of dispersion curves with the results calculated by 3-D exact theory. Free coupling vibrations of the cross-sectional plane of finite-sized shear mode FBAR plates are further studied with the derived 2-D theory. The results in this article show that the presented plate theory is accurate and efficient for the structural analyses of shear mode FBARs. Besides, the selection of aspect ratios can be used to avoid strong mode couplings, which is helpful for device designs.

中文翻译：

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二维板理论用于剪切模式FBAR耦合振动分析

近年来，由于对生物传感器的兴趣增加，剪切模式薄膜体声波谐振器（FBAR）迅速发展。本文从理论上分析和讨论了实际设备中不可避免的模式耦合效应。采用Mindlin逼近方法，利用幂级数沿板厚方向扩展位移场，得到二维板式方程组。通过比较色散曲线与3-D精确理论计算的结果，验证了板理论的准确性。利用导出的二维理论进一步研究了有限尺寸剪切模式FBAR板的横截面的自由耦合振动。本文的结果表明，所提出的板理论对于剪切模式FBAR的结构分析是准确而有效的。此外，可以使用宽高比的选择来避免强模式耦合，这对器件设计很有帮助。