A variational approach to a stationary free boundary problem modeling MEMS
Abstract
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 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.
Keywords
Cite
@article{arxiv.1409.2812,
title = {A variational approach to a stationary free boundary problem modeling MEMS},
author = {Philippe Laurencot and Christoph Walker},
journal= {arXiv preprint arXiv:1409.2812},
year = {2014}
}