Regularized model of post-touchdown configurations in electrostatic MEMS: Equilibrium analysis

• We propose a regularized model for electrostatic MEMS.
• Solutions are bounded and undergo additional dynamics after touchdown.
• Convergence to a new branch of equilibria, which is absent in the non regularized equations.
• The regularization equations have bistable equilibrium structure.

In canonical models of Micro-Electro Mechanical Systems (MEMS), an event called touchdown 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 propose 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 properties and equilibrium solutions of the regularized family of equations.