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Open AccessArticle

A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness

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Dipartimento di Ingegneria Industriale e dell’Informazione, University of Pavia, Via A. Ferrata 5, 27100 Pavia, Italy
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Dipartimento di Ingegneria dell’Informazione Infrastrutture Energia Sostenibile, “Mediterranea” University, Via Graziella Feo di Vito, I-89122 Reggio Calabria, Italy
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Dipartimento di Ingegneria Civile Energia Ambiente e Materiali, “Mediterranea” University, Via Graziella Feo di Vito, I-89122 Reggio Calabria, Italy
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1193; https://doi.org/10.3390/math7121193
Received: 5 November 2019 / Revised: 3 December 2019 / Accepted: 4 December 2019 / Published: 5 December 2019
In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of the existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured. View Full-Text
Keywords: circular membrane MEMS devices; electrostatic actuator; boundary non-linear second-order differential problems; singularities; mean curvature circular membrane MEMS devices; electrostatic actuator; boundary non-linear second-order differential problems; singularities; mean curvature
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Di Barba, P.; Fattorusso, L.; Versaci, M. A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness. Mathematics 2019, 7, 1193.

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