Working Paper Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 6 November 2019 / Approved: 8 November 2019 / Online: 8 November 2019 (10:33:32 CET)

How to cite: Di Barba, P.; Fattorusso, L.; Versaci, M. A 2D Electrostatic Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness. Preprints 2019, 2019110092 Di Barba, P.; Fattorusso, L.; Versaci, M. A 2D Electrostatic Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness. Preprints 2019, 2019110092

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 existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured.

Subject Areas

circular membrane mems devices; electrostatic actuator; boundary non-linear second-order differential problems; singularities; mean curvature

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