Numerical Modelling of Non-Linearities in MEMS Resonators

Zega, Valentina; Gattere, Gabriele; Koppaka, Saisneha; Alter, Anne L.; Vukasin, Gabrielle D.; Frangi, Attilio; Kenny, Thomas W.

doi:10.1109/jmems.2020.3026085

Cited by 20 publications

(26 citation statements)

References 67 publications

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“…1:2 internal resonance between the two modes can be triggered by driving the roll mode through the electrodes on the substrate. The two linear natural frequencies have an initial ratio of 1.926, which evolves to almost exactly 2 as the applied electrostatic bias increases and due to the electrostatic nonlinearities given by the parallel-plate electrostatic scheme 55 .…”

Section: Resultsmentioning

confidence: 99%

“…The implicit static condensation method validated by the authors on simple structures 41 , 55 is here applied to reduce the system to two degrees of freedom (i.e. the amplitudes of the two master roll and spurious-roll modes), thus dramatically reducing the computational effort without losing accuracy and physical meaning (see “ Methods ” section).…”

Section: Resultsmentioning

confidence: 99%

“…In the following, and according to the simplified numerical tool 56 proposed by the authors to compute fluid damping in MEMS resonant structures working in low pressure conditions such as in this case. Note that a nonlinear quality factor can in principle be also considered in the case of very large displacements of the proof mass with respect to the air gap between it and the fixed electrodes 55 .…”

Section: Resultsmentioning

confidence: 99%

“…2 , numerical curves in terms of displacements obtained by integrating Eqs. ( 1 ) and ( 2 ) are converted in terms of current as detailed in Zega et al 55 to simplify the comparison with experimental data.…”

Section: Resultsmentioning

confidence: 99%

“…In particular, the ICE applies to structures which undergo transformations which are no-longer infinitesimal, but still moderate. The approach has been verified on a double-ended tuning fork resonator experiencing both geometric, electrostatic and damping nonlinearities 55 , and represents a fast a priori multiphysics simulation tool able to reproduce the nonlinear dynamics caused by the interaction of two modes of a complex MEMS gyroscope test-structure without the need of calibration procedures. To the authors best knowledge this represents the first fast numerical predictive tool able to simulate a priori the internal resonance phenomenon including bifurcations of the periodic response in a complex structure and in general, the nonlinear dynamic behavior of MEMS devices.…”

Section: Introductionmentioning

confidence: 99%

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

Gobat

Zega

Fedeli

et al. 2021

Sci Rep

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Gobat

Zega

Fedeli

et al. 2021

Sci Rep

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Deep learning‐based reduced order models for the real‐time simulation of the nonlinear dynamics of microstructures

Fresca

Gobat

Fedeli

et al. 2022

Numerical Meth Engineering

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We propose a non‐intrusive deep learning‐based reduced order model (DL‐ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity snapshots are used to generate a POD‐Galerkin ROM which is subsequently exploited to generate the data, covering the whole parameter range, used in the training phase of the DL‐ROM. A convolutional autoencoder is employed to map the system response onto a low‐dimensional representation and, in parallel, to model the reduced nonlinear trial manifold. The system dynamics on the manifold is described by means of a deep feedforward neural network that is trained together with the autoencoder. The strategy is benchmarked against high fidelity solutions on a clamped‐clamped beam and on a real micromirror with softening response and multiplicity of solutions. By comparing the different computational costs, we discuss the impressive gain in performance and show that the DL‐ROM truly represents a real‐time tool which can be profitably and efficiently employed in complex system‐level simulation procedures for design and optimization purposes.

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