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

Paolo Di Barba, Luisa Fattorusso and Mario Versaci
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Paolo Di Barba: Dipartimento di Ingegneria Industriale e dell’Informazione, University of Pavia, Via A. Ferrata 5, 27100 Pavia, Italy
Luisa Fattorusso: Dipartimento di Ingegneria dell’Informazione Infrastrutture Energia Sostenibile, “Mediterranea” University, Via Graziella Feo di Vito, I-89122 Reggio Calabria, Italy
Mario Versaci: Dipartimento di Ingegneria Civile Energia Ambiente e Materiali, “Mediterranea” University, Via Graziella Feo di Vito, I-89122 Reggio Calabria, Italy

Mathematics, 2019, vol. 7, issue 12, 1-18

Abstract: 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.

Keywords: circular membrane MEMS devices; electrostatic actuator; boundary non-linear second-order differential problems; singularities; mean curvature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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