Fully Lagrangian modeling of MEMS with thin plates

Microelectromechanical systems (MEMS) sometimes use beam or plate shaped conductors that can be very thin-with h/LapO(10^-2-10 ^-3) (in terms of the thickness h and length L of the side of a square pate). Such MEMS devices find applications in microsensors, microactuators, microjets, microspeakers and other systems where the conducting plates or beams oscillate at very high frequencies. Conventional boundary element method (BEM) analysis of the electric field in a region exterior to such thin conductors can become difficult to carry out accurately and efficiently especially since MEMS analysis requires computation of charge densities (and then surface tractions) separately on the top and bottom surfaces of such plates. A new boundary integral equation (BIE) is proposed to handle the computation of charge densities for such high aspect ratio geometries. In the current work, this has been coupled with finite element method (FEM) to obtain the response behavior of devices made of such high aspect ratio structural members. This coupling of electrical and mechanical problem is carried out using a Newton scheme based on a Lagrangian description of both the mechanical and electrical domains