具有铰接顶板的三维MEMS的自由边界模型:固定情况

IF 0.5 4区数学 Q3 MATHEMATICS

Portugaliae Mathematica Pub Date : 2021-03-11 DOI:10.4171/pm/2067

K. Nik

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引用次数: 1

摘要

研究了三维静电MEMS器件的静态自由边界问题。该装置由刚性接地板和弹性顶板组成，弹性顶板在其边界处铰接，两板保持在不同的电压下。该模型将顶板变形的非局部四阶方程与两板间自由域静电势的拉普拉斯方程耦合在一起。耦合的强度由一个参数λ调谐，该参数与施加电压差的平方成正比。对于λ的小值，建立了稳定平稳解的存在性。当λ足够大时，得到平稳解的不存在性。

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On a free boundary model for three-dimensional MEMS with a hinged top plate: Stationary case

A stationary free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at different voltages. The model couples a nonlocal fourth-order equation for the deformation of the top plate to a Laplace equation for the electrostatic potential in the free domain between the two plates. The strength of the coupling is tuned by a parameter λ which is proportional to the square of the applied voltage difference. Existence of a stable stationary solution is established for small values of λ. Nonexistence of stationary solutions is obtained when λ is large enough.

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来源期刊

Portugaliae Mathematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.