<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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. </p></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.

Electrostatic field in terms of geometric curvature in membrane MEMS devices

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Electrostatic field in terms of geometric curvature in membrane MEMS devices"}

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...

Electrostatic field in terms of geometric curvature in membrane MEMS devices

Published Online: Jul 20, 2017

Page range: 165 - 184

Received: May 07, 2017

Accepted: Jun 16, 2017

DOI: https://doi.org/10.1515/caim-2017-0009

Keywords
mems, nems, electrostatic actuation, boundary semi-linear elliptic problems, green function, fixed-point theorem

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Electrostatic field in terms of geometric curvature in membrane MEMS devices

Published Online: Jul 20, 2017

Page range: 165 - 184

Received: May 07, 2017

Accepted: Jun 16, 2017

DOI: https://doi.org/10.1515/caim-2017-0009

Keywordsmems, nems, electrostatic actuation, boundary semi-linear elliptic problems, green function, fixed-point theorem

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
mems, nems, electrostatic actuation, boundary semi-linear elliptic problems, green function, fixed-point theorem