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Based on previous results of the existence, uniqueness, and regularity conditions for a continuous dynamic model for a parallel-plate electrostatic micro-electron-mechanical-systems with the fringing field, the purpose of this paper concerns a Galerkin-FEM procedure for deformable element deflection recovery. The deflection profiles are reconstructed by assigning the dielectric properties of the moving element. Furthermore, the device’s use conditions and the deformable element’s mechanical stresses are presented and discussed.

The Galerkin-FEM approach is based on weighted residuals, where the integrals appearing in the solution equation have been solved using the Crank–Nicolson algorithm.

Based on the connection between the fringing field and the electrostatic force, the proposed approach reconstructs the deflection of the deformable element, satisfying the conditions of existence, uniqueness and regularity. The influence of the electromechanical properties of the deformable plate on the method has also been considered and evaluated.

The developed analytical model focused on a rectangular geometry.

The device studied is suitable for industrial and biomedical applications.

This paper proposed numerical approach characterized by low CPU time enables the creation of virtual prototypes that can be analyzed with significant cost reduction and increased productivity.

The paper seeks to propose a specific approach based on Dynamic Analysis and Chaos Theory aiming to emphasize the differences into the eddy current signals obtained by related non‐destructive tests, when the inspected specimens have flaws with different shapes.

Non‐linear eddy current analysis is very useful for flaw detection in many in‐service inspections. State‐of‐the‐art technologies allow one to define position and depth of defects, but the shape identification is still an open problem. In this paper, experimental data have been subjected to a dynamical analysis in order to relate the trend of eddy current signals to the shape of analyzed defect.

In particular, a dynamical reconstruction by means of recurrence plots (RPs) has been carried out in order to detect analogies and differentiations between different eddy current signals. Moreover, cross‐correlation between RPs of a reference benchmark and testing eddy current signals has been applied in order to emphasize a different dynamical behaviour and to detect a particular flaw's shape. In this way, a real‐time algorithm for defect shape classification has been performed.

Proposed approach is very interesting, and it is an innovation in non‐destructive testing procedures. In fact, the shape identification of a flaw is still an open challenge. The proposed approach, based on dynamic analysis, gives the key to solve this particular ill‐posed problem, by introducing a relation between the eddy current measurements and the shape of defect existing in the inspected specimen. Very interesting preliminary results have been obtained.