Curvature Dependent Electrostatic Field in the Deformable MEMS Device: Stability and Optimal Control

IF 0.3 Q4 MATHEMATICS

Communications in Applied and Industrial Mathematics Pub Date : 2020-01-01 DOI:10.2478/caim-2020-0003

P. di Barba, L. Fattorusso, M. Versaci

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引用次数: 5

Abstract

Abstract The recovery of the membrane profile of an electrostatic micro-electro-mechanical system (MEMS) device is an important issue because, when applying an external voltage, the membrane deforms with the consequent risk of touching the upper plate of the device (a condition that should be avoided). Then, during the deformation of the membrane, it is useful to know if this movement admits stable equilibrium configurations. In such a context, our present work analyze the behavior of an electrostatic 1D membrane MEMS device when an external electric voltage is applied. In particular, starting from a well-known second-order elliptical semi-linear di erential model, obtained considering the electrostatic field inside the device proportional to the curvature of the membrane, the only possible equilibrium position is obtained, and its stability is analyzed. Moreover, considering that the membrane has an inertia in moving and taking into account that it must not touch the upper plate of the device, the range of possible values of the applied external voltage is obtained, which accounted for these two particular operating conditions. Finally, some calculations about the variation of potential energy have identified optimal control conditions.

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可变形MEMS器件中曲率相关静电场的稳定性与最优控制

摘要静电微机电系统（MEMS）器件的膜轮廓的恢复是一个重要问题，因为当施加外部电压时，膜会变形，从而有接触器件上板的风险（应避免这种情况）。然后，在膜的变形过程中，了解这种运动是否允许稳定的平衡配置是有用的。在这种背景下，我们目前的工作分析了静电1D膜MEMS器件在施加外部电压时的行为。特别地，从一个众所周知的二阶椭圆-半线性微分模型开始，考虑到器件内部的静电场与膜的曲率成比例，获得了唯一可能的平衡位置，并分析了其稳定性。此外，考虑到膜在移动时具有惯性，并考虑到它不能接触装置的上板，获得了施加的外部电压的可能值的范围，这解释了这两种特定的操作条件。最后，通过对势能变化的一些计算，确定了最优控制条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.