A variational approach to a stationary free boundary problem modeling MEMS

Philippe Laurençot, Christoph Walker
2016 E S A I M: Control, Optimisation and Calculus of Variations  
A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid ground plate. The model couples a non-local fourth-order equation for the elastic plate deflection to the harmonic electrostatic potential in the free domain between the elastic and the ground plate. The corresponding energy is non-coercive reflecting an
more » ... reflecting an inherent singularity related to a possible touchdown of the elastic plate. Stationary solutions are constructed using a constrained minimization problem. A by-product is the existence of at least two stationary solutions for some values of the applied voltage.
doi:10.1051/cocv/2015012 fatcat:agxkvcibv5fnlcmj4yvk7otm3q