声损耗对微机械谐振器品质因数的贡献
Contribution of Acoustic Losses in the Quality Factor of a Micromechanical Resonator
摘要：
对微机械（MEMS）环形谐振器的各种横向振动模式的声辐射损失进行了半解析研究。这种谐振器的品质因数Q在许多应用中是令人感兴趣的，并且取决于结构几何形状、与外部环境的相互作用以及封装方法。具有至少一个暴露于空气的表面的谐振器可以通过声辐射显示损耗，即使在微米尺寸下。已发表的实验结果表明，MEMS鼓谐振器的Q值中的声学损失占主导地位。在这项研究中，一个完善的数学技术来分析模型谐振器的振动模式和流体-结构相互作用的使用，和一个半分析程序计算Q由于声辐射损失，Qac，在任何振动模式概述。目前的技术包括计算精确的模态振型及其在计算Qac中的利用。计算了Qac对前15阶振型的依赖性。结果进行了比较，为最低的2个模式的固体圆形谐振器使用确切的模式形状的兰姆的近似模式形状。与已发表的实验结果相比，验证了该技术的预测效用，特别是对于声辐射似乎是Q的主要成分的较高模式。
英文摘要：
A semi-analytical study of the acoustic radiation losses associated with various transverse vibration modes of a micromechanical (MEMS) annular resonator is presented. The quality factor, Q, of such resonators is of interest in many applications and depends on structural geometry, interaction with the external environment, and the encapsulation method. Resonators with at least one surface exposed to air can display losses through acoustic radiation even at micro meter dimensions. Published experimental results suggest the dominance of acoustic losses in the Q of a MEMS drum resonator. In this study, a well established mathematical techniques to analytically model resonator vibration modes and fluid-structure interaction are used, and a semi-analytical procedure for computing Q due to acoustic radiation losses, Qac, in any vibrational mode outlined. Present technique includes calculation of the exact mode shape and its utilization in computing Qac. The dependence of Qac on the first 15 mode shapes is computed. Results are compared for the lowest 2 modes of a solid circular resonator using exact mode shapes to those of Lamb's approximate mode shapes. Comparison to published experimental results validates the predictive utility of the technique, especially for higher modes where acoustic radiation seems to be the dominant constituent of Q.
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