Electro-mechanical Coupling in MEMS: Modeling and Experimental Validation

This paper presents the advantages of a strong coupled formulation to model the electro-mechanical coupling appearing in MEMS. The classical modeling approach is to use a staggered methodology iterating between two different programs to obtain the solution of the coupled problem. In this research a strong coupled formulation is proposed and a tangent stiffness matrix of the whole problem is computed. Using this matrix, nonlinear algorithms such as the Riks-Crisfield algorithm may be applied to solve the static nonlinear problem and accurately determine the static pull-in voltage. Moreover, the natural frequencies may be computed around each equilibrium positions. The dynamic behavior of the structure may also be studied and two new parameters are defined: the dynamic pull-in voltage and the dynamic pull-in time. This strong coupled methodology deriving from variational principle may also be used for topology optimization and extended finite elements. The contribution presented here is based on the following two papers: 1. V. Rochus, D.J. Rixen, J.-C. Golinval, On the Advantages of Using a Strong Coupling Variational Formulation to Model Electro-Mechanical Problem, Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-systems EuroSime 2006, Como, Italia, 2006 2. V. Rochus, D.J. Rixen, J.-C. Golinval, Correlation of Experimental and Numerical Results on Electrostatically Actuated Micro-Beams, Ninth International Conference on Modeling and Simulation of Microsystems, Boston, USA, 2006