Derivation and Equilibrium Analysis of a Regularized Model for Electrostatic MEMS

• Main Authors: Lindsay, A. E, Lega, J, Glasner, K. B
• Format: Journal Article
• Language: English
• Published: 01-10-2013
• Subjects: Mathematics - Analysis of PDEs
• DOI: 10.48550/arxiv.1310.0422

In canonical models of Micro-Electro Mechanical Systems (MEMS), an event
called touch- down whereby the electrical components of the device come into
contact, is characterized by a blow up in the governing equations and a
non-physical divergence of the electric field. In the present work, we derive
novel regularized governing equations whose solutions remain finite at
touchdown and exhibit additional dynamics beyond this initial event before
eventually relaxing to new stable equilibria. We employ techniques from
variational calculus, dynamical systems and singular perturbation theory to
obtain a detailed understanding of the novel behaviors exhibited by the
regularized family of equations.