Dynamics and touchdown in electrostatic MEMS

A mathematical model of an idealized electrostatically actuated MEMS or NEMS device is presented for the purpose of studying the dynamics of the so-called "pull-in" instability. This arises when applied voltages are increased beyond a certain critical voltage where steady-state solutions cease to exist. A reduced one-dimensional nonlinear reaction-diffusion equation representing an idealized electrostatic structure is derived and analyzed. The coefficient tuning the nonlinear part determines existence of steady-state solutions. Questions about where, when, and how touchdown occurs are answered. A summary of new findings is presented and formal analytical results are compared with numerical approximations.