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A Case Study on the Numerical Solution and Reduced Order Model of MEMS

机译:MEMS的数值解和降阶模型的实例研究

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摘要

In this paper, we develop a numerical method with a reduced order techniquernbased on the Galerkin procedure to solve nonlinear partial differential equationsrnof MEMS devices. We apply an explicit numerical approach based on the finiterndifference method (FDM) to a reduced order model of the equation of micro-beamsrnand call it explicit-ROM. As a case study, we obtain the time response of a microbeamrnunder an electrostatic actuation and a mechanical shock with our method andrnthe reduced order method (ROM) developed in previous papers. We show ROMrnrequires taking the effect of higher order modes into consideration in order to resultrnin accurate response, while explicit-ROM greatly improves both accuracy and speedrnwith only the first mode, hence it is a straightforward approach that can be used in arnMEMS software to obtain very fast and accurate results.
机译:在本文中,我们基于Galerkin程序开发了一种具有降阶技术的数值方法来求解非线性偏微分方程。我们将基于有限差分法(FDM)的显式数值方法应用于微束方程的降阶模型,并将其称为显式ROM。作为案例研究,我们利用以前的方法开发的方法和降阶方法(ROM)获得了静电激励和机械冲击下微束的时间响应。我们展示了ROMrnrequires考虑到更高阶模式的影响,以便得到准确的响应,而显式ROM仅使用第一种模式就大大提高了准确性和速度,因此,它是一种简单的方法,可以在arnMEMS软件中使用以获得非常精确的结果。快速准确的结果。

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