Electrostatic-Elastic MEMS with Fringing Field: A Problem of Global Existence

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, I-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, 2021, vol. 10, issue 1, 1-18

Abstract: In this paper, we prove the existence and uniqueness of solutions for a nonlocal, fourth-order integro-differential equation that models electrostatic MEMS with parallel metallic plates by exploiting a well-known implicit function theorem on the topological space framework. As the diameter of the domain is fairly small (similar to the length of the device wafer, which is comparable to the distance between the plates), the fringing field phenomenon can arise. Therefore, based on the Pelesko–Driscoll theory, a term for the fringing field has been considered. The nonlocal model obtained admits solutions, making these devices attractive for industrial applications whose intended uses require reduced external voltages.

Keywords: electrostatic MEMS; fringing field; nonlinear elliptic models; fourth-order integro-differential models; partial differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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