Heterogeneous dielectric properties in MEMS models

Philippe Laurencot (1) , Christoph Walker (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IFAM - Institut für Angewandte Mathematik

An idealized electrostatically actuated microelectromechanical system (MEMS) involving an elastic plate with a heterogeneous dielectric material is considered. Starting from the electrostatic and mechanical energies, the governing evolution equations for the electrostatic potential and the plate deflection are derived from the corresponding energy balance. This leads to a free boundary transmission problem due to a jump of the dielectric permittivity across the interface separating elastic plate and free space. Reduced models retaining the influence of the heterogeneity of the elastic plate under suitable assumptions are obtained when either the elastic's plate thickness or the aspect ratio of the device vanishes.

Mots clés: vanishing aspect ratio; variational inequality; MEMS; free boundary problem; transmission problem

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurencot, Christoph Walker. Heterogeneous dielectric properties in MEMS models. SIAM Journal on Applied Mathematics, 2018, 78 (1), pp.504--530. ⟨10.1137/17M1117483⟩. ⟨hal-01555752⟩