Finite Differences for Recovering the Plate Profile in Electrostatic MEMS with Fringing Field

Global existence and uniqueness conditions for a dimensionless fourth-order integro-differential model for an electrostatic-elastic MEMS device with parallel plates and fringing field contribution were recently achieved by the Authors. Moving from this work, once the dielectric profile of the deformable plate according with experimental setups has been assigned, some technical conditions of applicability for the intended use of the device as well as the mechanical tension of the deformable plate are presented and discussed. Then, highlighting the link between the fringing field and the electrostatic force, finite differences were exploited for recovering the deformable plate profile according both global existence and uniqueness conditions. Moreover, the influence of the electro-mechanical properties of the deformable plate on both the numerical approach and on the intended uses of the device is discussed, comparing the results with experimental setups regarding pull-in voltage and electrostatic pressure.