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.
Highlights
Micro-Electro-Mechanical Systems revolutionized the consumer market for their small dimensions, high performances and low costs
A schematic view of the Mechanical Systems (MEMS) gyroscope test-structure employed in this work is reported in Fig. 1a, close-up views and geometrical dimensions are reported in the Supplementary Information for the sake of clarity
In the close-up views of Fig. 2b,d, it is evident that the Neimark–Sacker bifurcations predicted by the Reduced Order Models (ROMs) correctly delimit the experimental quasi-periodic region, further proving the accuracy of the proposed a priori simulation tool
Summary
Micro-Electro-Mechanical Systems revolutionized the consumer market for their small dimensions, high performances and low costs. 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, greatly speeding-up the solution phase and improving the design process of MEMS devices. Despite the great interest of the topic, a general a priori simulation tool that could predict in real-time the nonlinear dynamic behavior of complex MEMS structures like e.g. gyroscopes under different actuation conditions, is still missing. Such a tool would dramatically improve the design process and pave the way to a new class of sensors/ actuators experiencing complex nonlinear dynamic phenomena
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