Dynamic analysis of variable-geometry electrostatic microactuators
Dynamic analysis of variable-geometry electrostatic microactuators
复制标题
DOI：
10.1088/0960-1317/16/11/028
复制
发表时间：
2006-11-01
影响因子：
2.3
通讯作者：
Nayfeh, A.
中科院分区：
文献类型：
--
作者：
Najar, F.;Choura, S.;Nayfeh, A.
本文研究了一种基于微梁的静电微驱动器的动态特性。所考虑的微梁的横截面沿其长度变化。采用考虑中面拉伸和静电作用力引起的系统非线性的数学模型，对微束动力学进行了研究。采用微分求积法(DQM)和有限差分法(FDM)对偏微积分方程组进行离散，得到了不同微结构几何形状和不同电压下的频响曲线。我们表明，使用带有少量网格点的DQM，结合分别应用于空间导数和时间导数的有限差分方法，可以获得良好的动力学解的收敛。利用Floquet理论考察了这些解的稳定性。结果显示了微结构的动力学特性以及不同几何形状对微结构频响曲线的影响。我们首先证明了当网格点数在5到13之间变化时，当一个时间周期内的时间步数固定为100时，DQM-FDM离散动力学模型的收敛。然后将所提出的DQM-FDM离散化动态模型与最近报道的模型进行了比较。我们发现，微梁在其第一固有频率附近激励的频率响应曲线的形状对建立模型时所采用的近似非常敏感。最后，我们研究了不同的间隙尺寸、微束厚度和宽度对其硬化型和软化型频率响应曲线的影响。
This paper investigates the dynamic behavior of a microbeam-based electrostatic microactuator. The cross-section of the microbeam under consideration varies along its length. A mathematical model, accounting for the system nonlinearities due to mid-plane stretching and electrostatic forcing, is adopted and used to examine the microbeam dynamics. The differential quadrature method (DQM) and finite difference method (FDM) are used to discretize the partial-differential-integral equation and generate frequency-response curves for various microstructure geometries and different voltages. We show that the use of the DQM, with a few grid points, in conjunction with the FDM applied to the space derivatives and time derivatives, respectively, yields excellent convergence of the dynamic solutions. The stability of these solutions is examined using Floquet theory. Results are presented to display the dynamics and the effect of variable geometry on the frequency-response curves of the microstructure. We first demonstrate convergence of the DQM-FDM discretized dynamics model as the number of grid points is varied from 5 to 13, while the number of time steps in one time period is fixed at 100. The proposed DQM-FDM discretized dynamic model is then compared to recently reported models. We show that the shape of the frequency-response curves of the microbeam, excited near its first natural frequency, is very sensitive to the approximations employed in the construction of the model. Finally, we examine the effect of varying the gap size and the microbeam thickness and width on its frequency-response curves for hardening-type and softening-type behaviors.