An Investigation on the Effects of Contact in MEMS Oscillators

Guerrieri, A.; Frangi, Attilio; Falorni, Luca

doi:10.1109/jmems.2018.2875338

Cited by 19 publications

(10 citation statements)

References 55 publications

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“…a single Q value, for the whole structure. This assumption is of current use in MEMS community, and it has shown to be reliable for a number of test cases [78,79].…”

Section: Applicationsmentioning

confidence: 99%

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

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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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“…a single Q value, for the whole structure. This assumption is of current use in MEMS community, and it has shown to be reliable for a number of test cases [78,79].…”

Section: Applicationsmentioning

confidence: 99%

“…a single Q value, for the whole structure. This assumption is of current use in MEMS community, and it has shown to be reliable for a number of test cases [78,79]. The ROMS are derived thanks to the second-order DNF method, where the nonlinear mapping is truncated at second-order while the reduced dynamics is truncated at third-order.…”

Section: Applicationsmentioning

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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“…However, it is worth mentioning that FCs in MEMS might be associated with different phenomena. An example is discussed in [19] where FCs arise as a consequence of intermittent contact between deformable beams in a MEMS structure.…”

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confidence: 99%

Backbone curves, Neimark-Sacker boundaries and appearance of quasi-periodicity in nonlinear oscillators: application to 1:2 internal resonance and frequency combs in MEMS

et al. 2021

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Quasi-periodic solutions can arise in assemblies of nonlinear oscillators as a consequence of Neimark-Sacker bifurcations. In this work, the appearance of Neimark-Sacker bifurcations is investigated analytically and numerically in the specific case of a system of two coupled oscillators featuring a 1:2 internal resonance. More specifically, the locus of Neimark-Sacker points is analytically derived and its evolution with respect to the system parameters is highlighted. The backbone curves, solution of the conservative system, are first investigated, showing in particular the existence of two families of periodic orbits, denoted as parabolic modes. The behaviour of these modes, when the detuning between the eigenfrequencies of the system is varied, is underlined. The non-vanishing limit value, at the origin of one solution family, allows explaining the appearance of isolated solutions for the damped-forced system. The results are then applied to a Micro-Electro-Mechanical System-like shallow arch structure, to show how the analytical expression of the Neimark-Sacker boundary curve can be used for rapid prediction of the appearance of quasiperiodic regime, and thus frequency combs, in Micro-Electro-Mechanical System dynamics.

show abstract

“…a single Q value, for the whole structure. This assumption is of current use in MEMS community, and it has shown to be reliable for a number of test cases [80,81].…”

Section: Applicationsmentioning

confidence: 99%

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

et al. 2021

Self Cite

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.

show abstract

An Investigation on the Effects of Contact in MEMS Oscillators

Cited by 19 publications

References 55 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

Backbone curves, Neimark-Sacker boundaries and appearance of quasi-periodicity in nonlinear oscillators: application to 1:2 internal resonance and frequency combs in MEMS

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

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