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

In this paper, a stable numerical approach for recovering the membrane profile of a 2D Micro-Electric-Mechanical-Systems (MEMS) is presented. Starting from a well-known 2D nonlinear second-order differential model for electrostatic circular membrane MEMS, where the amplitude of the electrostatic fie...

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Bibliographic Details
Published in:Mathematics (Basel) 2020-04, Vol.8 (4), p.487
Main Authors: Versaci, Mario, Angiulli, Giovanni, Jannelli, Alessandra
Format: Article
Language:English
Subjects:
2D nonlinear second order differential model
electrostatic membrane MEMS devices
ghost solutions
Lobatto’s scheme
mean curvature
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Summary:In this paper, a stable numerical approach for recovering the membrane profile of a 2D Micro-Electric-Mechanical-Systems (MEMS) is presented. Starting from a well-known 2D nonlinear second-order differential model for electrostatic circular membrane MEMS, where the amplitude of the electrostatic field is considered proportional to the mean curvature of the membrane, a collocation procedure, based on the three-stage Lobatto formula, is derived. The convergence is studied, thus obtaining the parameters operative ranges determining the areas of applicability of the device under analysis.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8040487