Fully Lagrangian Modeling of Dynamics of MEMS With Thin Beams―Part I: Undamped Vibrations
Fully Lagrangian Modeling of Dynamics of MEMS With Thin Beams―Part I: Undamped Vibrations
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细梁 MEMS 动力学的完全拉格朗日建模 - 第一部分：无阻尼振动
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
S. Mukherjee
中科院分区：
文献类型：
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作者：
R. Ghosh;S. Mukherjee
微机电系统 (MEMS) 通常使用非常薄的梁或板状导体，h/L≈O(10 ―2 ―10 ―3 )（以梁或方形板边的厚度 h 和长度 L 表示）。此类 MEMS 器件可应用于微传感器、微致动器、微喷射、微扬声器以及导电梁或板以非常高的频率振荡的其他系统。对如此薄的导体外部区域的电场进行传统的边界元方法分析可能变得难以准确有效地进行，特别是因为 MEMS 分析需要分别计算此类梁的顶面和底面的电荷密度（然后是表面牵引力）。提出了一种新的边界积分方程来处理这种高纵横比几何形状的电荷密度的计算。在当前的工作中，这已与有限元方法相结合，以获得由此类高纵横比结构构件制成的设备的响应行为。这种电气和机械问题的耦合是使用基于电气和机械领域的拉格朗日描述的牛顿方案来实现的。本文给出了无阻尼耦合 MEMS 动态行为的数值结果。仔细研究了梁与地面之间的间隙对梁在增加电势下的机械响应的影响。配套论文中考虑了阻尼（Ghosh 和 Mukherjee，2009 年，“薄梁 MEMS 动力学的完全拉格朗日建模 - 第二部分：阻尼振动”，ASME J. Appl. Mech. 76，第 051008 页）。
Micro-electro-mechanical systems (MEMSs) often use beam or plate shaped conductors that can be very thin―with h/L≈O(10 ―2 ―10 ―3 ) (in terms of the thickness h and length L of the beam or side of a square plate). Such MEMS devices find applications in microsensors, micro-actuators, microjets, microspeakers, and other systems where the conducting beams or plates oscillate at very high frequencies. Conventional boundary element method analysis of the electric field in a region exterior to such thin conductors can become difficult to carry out accurately and efficiently―especially since MEMS analysis requires computation of charge densities (and then surface traction) separately on the top and bottom surfaces of such beams. A new boundary integral equation has been proposed to handle the computation of charge densities for such high aspect ratio geometries. In the current work, this has been coupled with the finite element method to obtain the response behavior of devices made of such high aspect ratio structural members. This coupling of electrical and mechanical problems is carried out using a Newton scheme based on a Lagrangian description of the electrical and mechanical domains. The numerical results are presented in this paper for the dynamic behavior of the coupled MEMS without damping. The effect of gap between a beam and the ground, on mechanical response of a beam subjected to increasing electric potential, is studied carefully. Damping is considered in the companion paper (Ghosh and Mukherjee, 2009, "Fully Lagrangian Modeling of Dynamics of MEMS With Thin Beams―Part II: Damped Vibrations," ASME J. Appl. Mech. 76, p. 051008).