Abstract
In this paper, a stable numerical approach for recovering the membrane profile of a 2D Micro-Electric-Mechanical-Systems (MEMS) is presented. Starting from a well-known 2D nonlinear second-order differential model for electrostatic circular membrane MEMS, where the amplitude of the electrostatic field is considered proportional to the mean curvature of the membrane, a collocation procedure, based on the three-stage Lobatto formula, is derived. The convergence is studied, thus obtaining the parameters operative ranges determining the areas of applicability of the device under analysis.
Highlights
Introduction and Problem StatementAt present, micro-components are essential in the embedded engineering applications.In particular, micro-transducers’ and micro-actuators’ results are of paramount importance due to their role of micro-devices’ interfaces [1,2]
A numerical approach based on a three-stage Lobatto technique for recovering the profile of the membrane in an electrostatic circular MEMS is proposed
Exploited as a numerical collocation technique for the resolution of boundary value problem (BVP), this procedure has been preferred to shooting methods because it usually requires the integration of IVPs being heavily unstable
Summary
Micro-components are essential in the embedded engineering applications. In particular, micro-transducers’ and micro-actuators’ results are of paramount importance due to their role of micro-devices’ interfaces [1,2]. It consists of a nonlinear ordinary second-order differential equation (ODE) whose independent variable is the profile of the membrane u(r ) (characterized by a singularity 1/r) with suitable conditions on both u(r ) and du(r )/dr appropriately chosen This BVP has been studied in [22] where an algebraic condition ensuring the existence of the solution (depending on both V and the electromechanical properties of the material constituting the membrane) has been derived. After a suitable rearranging of the analytical model described above, the convergence of the proposed numerical procedure has been studied In this way, the ranges of validity of the characteristic parameters (which depend on both V and by the electromechanical properties of the material constituting the membrane) have been derived.
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