An efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems
An efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems
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DOI：
10.1016/j.jsv.2014.03.040
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发表时间：
2014-09
影响因子：
4.7
通讯作者：
H. Grigg;B. Gallacher
中科院分区：
文献类型：
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作者：
H. Grigg;B. Gallacher
高共振器的设计，如木琴杆谐振器（xbr），能够使用微机电系统（MEMS）工艺制造，鉴于依赖于其可用性和性能的系统的广泛和快速增长的使用，具有相当大的兴趣。本文研究了一种XBR的振动分析和优化，并将该方法直接推广到其他平面框架和更复杂的结构。详细讨论了瑞利-里兹方法，首先处理离散情况，然后开发并应用l -框架结构的运动学过程。在转向XBR案例之前，将重点放在瑞利-里兹程序的几何解释和对该方法的直观理解上。在建立了系统动力学近似之后，将结果与基材中弹性波传播的解析模型结合使用，以获得supportQfactor的估计。给出了固有频率、模态振型和supportQvalues，并将其与相同问题的有限元模型进行了比较，结果非常一致，计算成本大大降低。在文献中，首次验证和量化了XBR设计背后的几何阻抗调谐原理，包括对制造误差的敏感性。
The design of high-Qresonators such as Xylophone Bar Resonators (XBRs) capable of being fabricated using Micro-Electro-Mechanical Systems (MEMS) processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance. This paper is concerned with vibration analysis andQoptimisation of an XBR, with the method extending directly to other planar frames and straightforwardly to more complex structures. The Rayleigh–Ritz method is discussed in some detail, first treating the discrete case, followed by developing and applying a kinematical procedure to an L-frame structure. Attention is given to geometric interpretation of the Rayleigh–Ritz procedure and to developing an intuitive understanding the method before turning to the XBR case. Having developed an approximation for system dynamics, the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the supportQfactor. Natural frequencies, mode shapes, and supportQvalues are presented and compared to Finite Element models of the same problem, with excellent agreement observed at substantially lower computational cost. For the first time in the literature, the geometric impedance tuning principle underlying the XBR design is validated and quantified, including sensitivity to manufacturing error.