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

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

Dipartimento di Ingegneria Industriale e dell’Informazione

Dipartimento di Ingegneria dell’Informazione Infrastrutture Energia Sostenibile

Dipartimento di Ingegneria Civile Energia Ambiente e Materiali

Communications in Applied and Industrial Mathematics

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

The recovery of the membrane profile of an electrostatic micro-electro-mechanical system (MEMS) device is an important issue because, when applying an external...

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

Published Online: Oct 31, 2020

Page range: 35 - 54

DOI: https://doi.org/10.2478/caim-2020-0003

Keywords
MEMS DEVICE, ELECTROSTATIC ACTUATORS, BOUNDARY SEMI-LINEAR ELLIPTC MODELS, CURVATURE

© 2020 Paolo Di Barba et al., published by Sciendo

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

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

Published Online: Oct 31, 2020

Page range: 35 - 54

DOI: https://doi.org/10.2478/caim-2020-0003

KeywordsMEMS DEVICE, ELECTROSTATIC ACTUATORS, BOUNDARY SEMI-LINEAR ELLIPTC MODELS, CURVATURE

© 2020 Paolo Di Barba et al., published by Sciendo

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

Keywords
MEMS DEVICE, ELECTROSTATIC ACTUATORS, BOUNDARY SEMI-LINEAR ELLIPTC MODELS, CURVATURE