Tailoring the nonlinear response of MEMS resonators using shape optimization

Li, Lily L.; Polunin, Pavel M.; Dou, Suguang; Shoshani, Oriel; Strachan, B. Scott; Jensen, Jakob Søndergaard; Shaw, Steven W.; Turner, Kimberly L.

doi:10.1063/1.4976749

Cited by 44 publications

(21 citation statements)

References 21 publications

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“…MEMS structures are generally actuated at resonance, they are subjected to geometric nonlinearities due to large transformations and have very small damping values as they operate in near-vacuum packages, hence showing highly nonlinear dynamical features that are rarely observed at the macro scale [55,56,57,58,59,60]. Furthermore, nonlinear dynamic properties of MEMS can be tailored to yield performance that would not be accessible through operation in the linear regime [61,62,63,64]. A remarkable example of successful application of nonlinear mode interaction for the development of highly efficient mechanical filters is for instance reported in [65].…”

Section: Introductionmentioning

confidence: 99%

Model Order Reduction based on Direct Normal Form: Application to Large Finite Element MEMS Structures Featuring Internal Resonance

Opreni

Vizzaccaro

Frangi

et al. 2021

Preprint

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Dimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on direct normal form computation for large finite element (FE) models is here detailed. The main advantage resides in operating directly from the physical space, hence avoiding the computation of the complete eigenfunctions spectrum. Explicit solutions are given, thus enabling a fully non-intrusive version of the reduction method. The reduced dynamics is obtained from the normal form of the geometrically nonlinear mechanical problem, free of non-resonant monomials, and truncated to the selected master coordinates, thus making a direct link with the parametrisation of invariant manifolds. The method is fully expressed with a complex-valued formalism by detailing the homological equations in a systematic manner, and the link with real-valued expressions is established. A special emphasis is put on the treatment of second-order internal resonances and the specific case of a 1:2 resonance is made explicit. Finally, applications to large-scale models of Micro-Electro-Mechanical structures featuring 1:2 and 1:3 resonances are reported, along with considerations on computational efficiency.

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Section: Introductionmentioning

confidence: 99%

Model Order Reduction based on Direct Normal Form: Application to Large Finite Element MEMS Structures Featuring Internal Resonance

Opreni

Vizzaccaro

Frangi

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…MEMS structures are generally actuated at resonance, and they are subjected to geometric nonlinearities due to large transformations and have very small damping values as they operate in near-vacuum packages, hence showing highly nonlinear dynamical features that are rarely observed at the macroscale [55][56][57][58][59][60]. Furthermore, nonlinear dynamic properties of MEMS can be tailored to yield perfor-mance that would not be accessible through operation in the linear regime [61][62][63][64]. A remarkable example of successful application of nonlinear mode interaction for the development of highly efficient mechanical filters is for instance reported in [65].…”

Section: Introductionmentioning

confidence: 99%

Model order reduction based on direct normal form: application to large finite element MEMS structures featuring internal resonance

et al. 2021

View full text Add to dashboard Cite

Dimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on direct normal form computation for large finite element (FE) models is here detailed. The main advantage resides in operating directly from the physical space, hence avoiding the computation of the complete eigenfunctions spectrum. Explicit solutions are given, thus enabling a fully non-intrusive version of the reduction method. The reduced dynamics is obtained from the normal form of the geometrically nonlinear mechanical problem, free of non-resonant monomials, and truncated to the selected master coordinates, thus making a direct link with the parametrisation of invariant manifolds. The method is fully expressed with a complex-valued formalism by detailing the homological equations in a systematic manner, and the link with real-valued expressions is established. A special emphasis is put on the treatment of second-order internal resonances and the specific case of a 1:2 resonance is made explicit. Finally, applications to large-scale models of micro-electro-mechanical structures featuring 1:2 and 1:3 resonances are reported, along with considerations on computational efficiency.

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“…The optimization technique with the biggest potentialities of application in the inertial MEMS industry is structural size optimization: in this approach, the dimensions and positions of the mechanical elements composing the structure are parametrized by a set of design variables, which are then optimized by employing usual methods for numerical optimization, such as gradient-based [ 15 ] or stochastic/evolutionary techniques [ 16 , 17 ]. Size optimization has been applied to the design of several MEMS devices, e.g., to extend the operational frequency range in piezoelectric MEMS energy harvesters [ 18 ], to tailor mechanical nonlinearities through non-uniform beam profiles [ 19 ], or to improve temperature stability of tuning fork resonators through slots in the resonator beams [ 20 ].…”

Section: Introductionmentioning

confidence: 99%

Rapid Prototyping of Inertial MEMS Devices through Structural Optimization

Giannini

Bonaccorsi

Braghin

2021

Sensors

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In this paper, we propose a novel design and optimization environment for inertial MEMS devices based on a computationally efficient schematization of the structure at the a device level. This allows us to obtain a flexible and efficient design optimization tool, particularly useful for rapid device prototyping. The presented design environment—feMEMSlite—handles the parametric generation of the structure geometry, the simulation of its dynamic behavior, and a gradient-based layout optimization. The methodology addresses the design of general inertial MEMS devices employing suspended proof masses, in which the focus is typically on the dynamics associated with the first vibration modes. In particular, the proposed design tool is tested on a triaxial beating-heart MEMS gyroscope, an industrially relevant and adequately complex example. The sensor layout is schematized by treating the proof masses as rigid bodies, discretizing flexural springs by Timoshenko beam finite elements, and accounting for electrostatic softening effects by additional negative spring constants. The MEMS device is then optimized according to two possible formulations of the optimization problem, including typical design requirements from the MEMS industry, with particular focus on the tuning of the structural eigenfrequencies and on the maximization of the response to external angular rates. The validity of the proposed approach is then assessed through a comparison with full FEM schematizations: rapidly prototyped layouts at the device level show a good performance when simulated with more complex models and therefore require only minor adjustments to accomplish the subsequent physical-level design.

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Tailoring the nonlinear response of MEMS resonators using shape optimization

Cited by 44 publications

References 21 publications

Model Order Reduction based on Direct Normal Form: Application to Large Finite Element MEMS Structures Featuring Internal Resonance

Model Order Reduction based on Direct Normal Form: Application to Large Finite Element MEMS Structures Featuring Internal Resonance

Model order reduction based on direct normal form: application to large finite element MEMS structures featuring internal resonance

Rapid Prototyping of Inertial MEMS Devices through Structural Optimization

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