Regularized model of post-touchdown configurations in electrostatic MEMS: Interface dynamics

Interface dynamics of post-contact states in regularized models of electrostatic-elastic interactions are analysed. A canonical setting for our investigations is the field of Micro-Electromechanical Systems (MEMS) in which flexible elastic structures may come into physical contact due to applied Coulomb forces. We study the dynamic features of a recently derived regularized model (Lindsay, A. E. et al. 2014 Regularized model of post-touchdown configurations in electrostatic MEMS: equilibrium analysis. Physica D), which describes the system beyond the quenching singularity associated with touchdown, that is after the components of the device have come together. We build on our previous investigations of steady-state solutions by describing how the system relaxes towards these equilibria. This is accomplished by deriving a reduced dynamical system that governs the evolution of the contact set, thereby providing a detailed description of the intermediary dynamics associated with this bistable system. The analysis yields important practical information on the timescales of equilibration.