Reduced order modelling and experimental validation of a MEMS gyroscope test-structure exhibiting 1:2 internal resonance

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.

Symmetry-Breaking-Induced Frequency Combs in Graphene Resonators

“…By driving the drum at elevated blue laser powers and performing upward frequency sweeps, we observe in Figure b a butterfly-shaped response, consisting of two Duffing-like asymmetric resonances, one of which bending to lower and the other to higher frequency, indicating that one of the split peaks experiences a spring softening, and the other a spring hardening nonlinearity (similar responses have been observed in other nonlinear resonators undergoing IR − ). Interestingly, at the maximum drive level (10 dBm), the strong coupling between the resonant modes yields the emergence of a third peak in the middle of the split region at frequency f IR = 22.73 MHz (see Figure c).…”

“…To investigate the spectral characteristics of the quasi-periodic oscillations, we swept the excitation frequency Ω in the spectral neighborhood of the region confined by the two Neimark bifurcations and analyzed the time response of the nonlinear equations, similar to ref . Figure d shows the frequency content of the simulated time signal inside and outside this region.…”

Frequency combs in a MEMS resonator featuring 1:2 internal resonance: ab initio reduced order modelling and experimental validation

“…This method has been recently tailored for MEMS structures exhibiting damping, geometric and electrostatic nonlinearities. In particular, a very good agreement between experiments and numerical predictions has been shown in [92] for two double-ended-tuning-fork resonators electrostatically actuated according to their first bending mode and in [27] for a MEMS gyroscope test structure exhibiting 1:2 internal resonance.…”

Symmetry-breaking induced frequency combs in graphene resonators

“…To investigate the spectral characteristics of the quasi-periodic oscillations, we swept the excitation frequency Ω in the spectral neighborhood of the region confined by the two Neimark bifurcations, and analyzed the time response of the nonlinear equations, similar to [33]. Figure 3-d shows the frequency content of the simulated time signal inside and outside this region.…”