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Correlation of Experimental and Numerical Results on Electrostatically Actuated Micro-Beams

V. Rochus, D.J. Rixen and J.-C. Golinval
university of Li├Ęge, BE

Keywords:
electro-mechanical coupling, finite element method, electrostatic force

Abstract:
The aim of this paper is to validate numerical simulations of electromechanical coupling in micro-structures using some experimental results. The micro-structures studied here consist in a micro-bridge and two cantilever beams. Multi-physics simulations of micro-electro-mechanical systems (MEMS) based on the finite element method (FEM) are used to model the strongly coupled electro-mechanical interactions and to perform static analyses taking into account large displacements.
 
Classical methods used to simulate coupling between electric and mechanical fields are commonly based on staggered procedures, which consist in computing quasi-static configurations using two separate models. In this modeling research, a fully coupled electro-mechanical FE formulation is proposed, which allows to compute static equilibrium positions in a non-staggered way, and which provides fully consistent tangent stiffness matrices. The fully coupled methodology provides more reliable results than staggered methods.
 
The first example considered here is the micro-bridge. The beam is buckled upside. A prestress has to be added in the finite element model to simulate the observed geometry. Starting from the buckled configuration a voltage is applied between the electrodes and the beam is electrostatically actuated. The electro-mechanical problem is resolved by using the strong coupled electro-mechanical finite elements formulation with a Riks-Crisfield algorithm. The second example is a cantilever beam fabricated in the same layer as the micro-bridge. The displacement of the extremity of the beam due to the electrostatic actuation is computed. The second cantilever beam is realised in another structural layer. The beam has an initial deformation downward. To obtain a deformed shape of the beam at the initial configuration some gradient of prestress has to be taken into account. In all the cases treated here the numerical results are in very good agreement with the experimental results.

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