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.

Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

“…, 2021 ). In (17), the dependence on V of the action control determines the E in the device, which, in turn, generates an electrostatic pressure that moves the deformable plate ( Di Barba et al ., 2022 ; Bahreman et al ., 2019 ; Das and Bhushan, 2023 ) .…”

“…Equation (23) has been thoroughly studied in Di Barba et al. (2022), where the existence/uniqueness and regularity results for w have been obtained.…”

“…A dimensionless dynamic model of the device was recently studied with E ff also considering the effects of the stretching and stiffness of the d-microplate (Di Barba et al. , 2022; Manvi and Swamy, 2022), whose independent variable represents the deflection of the d-microplate.…”

“…, 2022; Manvi and Swamy, 2022), whose independent variable represents the deflection of the d-microplate. However, its complexity does not allow explicit resolution but only the obtaining of conditions to be satisfied to guarantee the existence, uniqueness and regularity of the deflection of the microplate (Di Barba et al. , 2022).…”

“…Therefore, starting from Di Barba et al. (2022), we propose the numerical recovery of the deflection of the d-microplate that does not represent ghost solution [i.e.…”