Vanishing aspect ratio limit for a fourth-order mems model

TL;DR

This paper rigorously justifies the small aspect ratio limit in a complex MEMS model that includes bending effects, extending the mathematical understanding of MEMS behavior as the aspect ratio approaches zero.

Contribution

It provides a rigorous mathematical proof for the derivation of the small aspect ratio model from a more complex MEMS model with bending effects.

Findings

Rigorous justification of the small aspect ratio limit

Extension of MEMS modeling to include bending effects

Mathematical validation of the simplified wave/beam equation

Abstract

So far most studies on mathematical models for microelectromechanical systems (MEMS) are focused on the so-called small aspect ratio model which is a wave or beam equation with a singular source term. It is formally derived by setting the aspect ratio equal to zero in a more complex model involving a moving boundary. A rigorous justification of this derivation is provided here when bending is taken into account.