Solution Properties of a New Dynamic Model for MEMS with Parallel Plates in the Presence of Fringing Field

Abstract

In this paper, starting from a well-known nonlinear hyperbolic integro-differential model of the fourth order describing the dynamic behavior of an electrostatic MEMS with a parallel plate, the authors propose an upgrade of it by formulating an additive term due to the effects produced by the fringing field and satisfying the Pelesko–Driscoll theory, which, as is well known, has strong experimental confirmation. Exploiting the theory of hyperbolic equations in Hilbert spaces, and also utilizing Campanato’s Near Operator Theory (and subsequent applications), results of existence and regularity of the solution are proved and discussed particularly usefully in anticipation of the development of numerical approaches for recovering the profile of the deformable plate for a wide range of applications.

Keywords

• MEMS with deformable plate
• hyperbolic dimensionless fourth-order integro-diffferential dynamic model
• nonlinearities
• Pelesko–Driscoll’s approach for fringing field modeling
• Campanato’s near operator theory