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Abstract Micro-Electro-Mechanical Systems revolutionized the consumer market for their small dimensions, high performances and low costs. In recent years, the evolution of the Internet of Things is posing new challenges to MEMS designers that have to deal with complex multiphysics systems experiencing highly nonlinear dynamic responses. To be able to simulate a priori and in real-time the behavior of such systems it is thus becoming mandatory to understand the sources of nonlinearities and avoid them when harmful or exploit them for the design of innovative devices. In this work, we present the first numerical tool able to estimate a priori and in real-time the complex nonlinear responses of MEMS devices without resorting to simplified theories. Moreover, the proposed tool predicts different working conditions without the need of ad-hoc calibration procedures. It consists in a nonlinear Model Order Reduction Technique based on the Implicit Static Condensation that allows to condense the high fidelity FEM models into few degrees of freedom, thus greatly speeding-up the solution phase and improving the design process of MEMS devices. In particular, the 1:2 internal resonance experienced in a MEMS gyroscope test-structure fabricated with a commercial process is numerically investigated and an excellent agreement with experiments is found.

The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam).