An Arbitrary Lagrangian Eulerian Approach for Air-Structure Interaction Problems: an Application to MEMS Micromirrors

  • Di Cristofaro, Daniele (Politecnico di Milano)
  • Cremonesi, Massimiano (Politecnico di Milano)
  • Frangi, Attilio (Politecnico di Milano)

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Micro-Electro-Mechanical Systems (MEMS) are devices that allow us to connect the digital world with the real world. In the context of MEMS micromirrors design, quantitative methods are important when trying to estimate system parameters, because the high cost of fabrication makes trial-and-error methods difficult to use. For systems that operate at resonance such as MEMS micromirrors, the quality factor Q of the drive mode [1] of the device is a key parameter for the quantification of dissipation. In the present investigation, we focus on the evaluation of energy losses due to fluid-damping, in particular on devices that work in air and with ambient pressure. With the aim to predict Q associated with dissipation in MEMS micromirrors subjected to large amplitude vibrations, we here develop and validate an Arbitrary Lagrangian Eulerian (ALE) finite element solver for the Navier Stokes equations [2]. The features of the solver we propose are the adoption of a Chorin-Temam scheme to speed up the computational time and the implementation of a Streamline-Upwind-Petrov-Galerkin (SUPG) finite element stabilisation scheme for the spatial discretisation. The harmonic movement of the device is apriori computed as the nonlinear normal mode of the mirror using the recently developed theory of invariant manifolds [3, 4]. The velocity field on the surface of the solid is then applied as a boundary condition to the mirror surface during the ALE analysis. Two types of micromirror’s architectures have been studied as benchmark cases for the proposed ALE numerical solver. The results obtained with Micromirror 1 show that the numerical Q factor underestimates the experimental one, with a relative error of 10% at low amplitude, while at larger angles the difference increases to 17% due to a stronger nonlinear behaviour. For Micromirror 2, the numerical Q factor slightly overestimates the experimental data, with a maximum relative error of 3%.