2014/09/09 by Philippe Laurençot, Philippe Laurencot, Laurencot, Philippe +2
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in engineering #math.AP
paper · pdf · doi:10.48550/arxiv.1409.2812
arxiv created 2014/09/09 · openalex publication_date 2014/09/09 · arxiv updated 2014/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.