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Solution Properties of a New Dynamic Model for MEMS with Parallel Plates in the Presence of Fringing Field

Author

Listed:
  • 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)

Abstract

In this paper, starting from a well-known nonlinear hyperbolic integro-differential model of the fourth order describing the dynamic behavior of an electrostatic MEMS with a parallel plate, the authors propose an upgrade of it by formulating an additive term due to the effects produced by the fringing field and satisfying the Pelesko–Driscoll theory, which, as is well known, has strong experimental confirmation. Exploiting the theory of hyperbolic equations in Hilbert spaces, and also utilizing Campanato’s Near Operator Theory (and subsequent applications), results of existence and regularity of the solution are proved and discussed particularly usefully in anticipation of the development of numerical approaches for recovering the profile of the deformable plate for a wide range of applications.

Suggested Citation

  • Paolo Di Barba & Luisa Fattorusso & Mario Versaci, 2022. "Solution Properties of a New Dynamic Model for MEMS with Parallel Plates in the Presence of Fringing Field," Mathematics, MDPI, vol. 10(23), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4541-:d:990015
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    References listed on IDEAS

    as
    1. Muhammad Aslam Noor & Khalida Inayat Noor, 2021. "Some New Classes of Higher Order Strongly Generalized Preinvex Functions," Springer Optimization and Its Applications, in: Ioannis N. Parasidis & Efthimios Providas & Themistocles M. Rassias (ed.), Mathematical Analysis in Interdisciplinary Research, pages 573-588, Springer.
    2. Mario Versaci & Giovanni Angiulli & Alessandra Jannelli, 2020. "Recovering of the Membrane Profile of an Electrostatic Circular MEMS by a Three-Stage Lobatto Procedure: A Convergence Analysis in the Absence of Ghost Solutions," Mathematics, MDPI, vol. 8(4), pages 1-19, April.
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