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

Abstract

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.

Keywords

• electrostatic membrane MEMS devices
• 2D nonlinear second order differential model
• mean curvature
• Lobatto’s scheme
• ghost solutions