薄膜MEMS器件中几何曲率的静电场

IF 0.3 Q4 MATHEMATICS Communications in Applied and Industrial Mathematics Pub Date : 2017-03-28 DOI:10.1515/caim-2017-0009

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

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引用次数: 32

摘要

摘要本文在一维膜微机电系统(MEMS)理论框架下，给出了稳态静电驱动下膜变形u解的存在唯一性问题的形式化形式。特别地，我们提出了电场大小E与膜曲率成正比的新模型，并通过Schauder-Tychono不动点应用得到了存在性结果，并建立了唯一性条件。最后，进行了数值试验来进一步支持分析结果。

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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Electrostatic field in terms of geometric curvature in membrane MEMS devices

Abstract In this paper we present, in a framework of 1D-membrane Micro-Electro-Mechanical- Systems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steady- state case. In particular, we propose a new model in which the electric field magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychono's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried out to further support the analytical results.

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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 Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments.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.