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

Purpose: 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. Design/methodology/approach: 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. Findings: 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. Research limitations/implications: The developed analytical model focused on a rectangular geometry. Practical implications: The device studied is suitable for industrial and biomedical applications. Originality/value: 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.