On a Free Boundary Model for Three-Dimensional MEMS with a Hinged Top Plate I: Stationary Case
Analysis of PDEs
2021-03-12 v1
Abstract
A stationary free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at different voltages. The model couples a nonlocal fourth-order equation for the deformation of the top plate to a Laplace equation for the electrostatic potential in the free domain between the two plates. The strength of the coupling is tuned by a parameter which is proportional to the square of the applied voltage difference. Existence of a stable stationary solution is established for small values of . Nonexistence of stationary solutions is obtained when is large enough.
Keywords
Cite
@article{arxiv.2103.06772,
title = {On a Free Boundary Model for Three-Dimensional MEMS with a Hinged Top Plate I: Stationary Case},
author = {Katerina Nik},
journal= {arXiv preprint arXiv:2103.06772},
year = {2021}
}