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首页> 外文期刊>Sensors Journal, IEEE >Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers
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Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers

机译：电容式微加工超声换能器中的圆形微孔板的静电静电分析

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摘要

The active structural component of a capacitive micromachined ultrasonic transducer (CMUT) is the top plate which vibrates under the influence of a time-varying electrostatic force thereby producing ultrasound waves of the desired frequency in the surrounding medium. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electrostatics-structure coupling aspect in the design of these devices. This paper presents an approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear. Traditionally, finite element simulations using some commercial software such as ANSYS are employed to determine the structural deflections caused by electrostatic forces. Since the structural deformation alters the electrostatic field, a coupled-field simulation is required wherein the electrostatic mesh is continuously updated to coincide with the deflection of the structure. Such simulations are extremely time consuming, in addition to being nontransparent and somewhat hard to implement. We employ the classical thin-plate theory which is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. We solve the thin-plate electrostatic-elastic equation using the Galerkin-weighted residual technique, under the assumption that the deflections are small in comparison to the thickness of the plate. The evaluation of the electrostatic force between the two plates is simplified due to the fact that the electrostatic gap is much smaller than the lateral dimensions of the device. The results obtained are compared to those found from ANSYS simulations and an excellent agreement is observed between the two. The pull-in volt-n-nage predicted by our model is close to the value predicted by ANSYS simulations.
机译：电容微机械超声换能器（CMUT）的有源结构组件是顶板，该顶板在时变静电力的作用下振动，从而在周围介质中产生所需频率的超声波。由于结构变形会改变静电力，因此对依靠静电驱动的MEMS器件进行分析非常复杂，从而重新分布和修改了施加的载荷。因此，在这些器件的设计中必须考虑静电-结构耦合方面。本文提出了一种固有的非线性静电力引起的薄的，夹紧的圆形板的静态挠度的近似解析解。传统上，使用一些商用软件（例如ANSYS）进行有限元模拟，以确定由静电力引起的结构变形。由于结构变形会改变静电场，因此需要进行耦合场模拟，其中会不断更新静电网格，以与结构的变形相一致。除了不透明并且难以实现之外，这种模拟非常耗时。我们采用经典的薄板理论，当板的直径与厚度之比非常大时就足够了，这种情况在许多MEMS器件（尤其是CMUT）中普遍存在。我们在假设挠度与板厚相比较小的情况下，使用Galerkin加权残差技术求解薄板静电弹性方程。由于静电间隙远小于设备的横向尺寸，因此简化了两块板之间静电力的评估。将获得的结果与从ANSYS仿真中发现的结果进行比较，并且观察到两者之间的一致性很好。我们的模型预测的吸合电压n值接近于ANSYS仿真预测的值。

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