Coupled Planar Electromechanical Analysis Based on Finite-Deformation Beam Bending

Abstract eng:
Electrostatically actuated micro and nano scale beams serve as a core part in many micro- and nanoelectromechanical systems (MEMS/NEMS) based applications including optical and electrical switches, resonators, diffractive elements, and chemical and biological sensors. Slender beam-like structures are attractive due to their small size, high sensitivity and simplicity of fabrication, while electrostatic actuation remains the most widely used due to favorable scaling laws at the micro scale, low power consumption and potential for integration in integrated circuits. The common, yet computationally intensive, approach for analysis of coupled electromechanical problems describing the behavior of these structures is to consider three-dimensional elastic and electrostatic continua. Alternatively, simplified approaches based on order reduction of the elastic domain to compact structural beam models are combined with approximate formulas for the electrostatic forces, often developed on an ad hoc basis. However, three-dimensional electrostatic fields may generate complex patterns of distributed loading on the solid that vary rapidly in space and time, rendering such a simplified approach ineffective. In addition, nonlinear effects become more pronounced with scale reduction. In the present work, we implement rigorous structural reduction procedures to consistently convert continuum electrostatic forces to the form required by the structural representation, in the framework of finite deformation, geometrically exact, planar beam bending. This approach facilitates the solution of problems that would otherwise pose formidable challenges. The use of appropriate structural models economizes the computation and provides insight into the electromechanical behavior, while preserving accuracy comparable with continua representations.

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