Reduced order modelling of the non-linear stiffness in MEMS resonators

Frangi, Attilio; Gobat, Giorgio

doi:10.1016/j.ijnonlinmec.2019.07.002

Cited by 59 publications

(55 citation statements)

References 33 publications

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“…The Implicit Condensation and Expansion (ICE) method has been first introduced by McEwan, Gordon and Hollkamp [38,39,48,40], and recently used by Kuether et al [42], and Frangi and Gobat [41]. As compared to the STEP method, where a series of static prescribed displacements are used in order to get the values of the modal coupling coefficients g p i j and h p i jk given in Eq.…”

Section: Ice Methods and Stress Manifoldmentioning

confidence: 99%

“…Material properties are selected as: density ρ = 7800kg.m −3 , Young modulus E = 2.1e+11 Pa, whereas the Poisson ratio is selected as ν = 0 in order to better mimic the assumptions of the theory of beams (see e.g. [41]).…”

Section: A Clamped-clamped Beammentioning

confidence: 99%

“…The second one relies on applying a series of static selected forces, and has been called the implicit condensation and expansion (ICE) method [38,39,40]. From the loadings and resulting large-amplitude displacements, a so-called stress manifold can be constructed in order to reduce the dynamics [41]. A main advantage of these two procedures (STEP and ICE) thus relies in their versatility and ease-of-use due this non-intrusive characteristics.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reduced order models for geometrically nonlinear structures: Assessment of implicit condensation in comparison with invariant manifold approach

Shen

Béreux

Frangi

et al. 2021

European Journal of Mechanics - A/Solids

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A comparison between two methods to derive reduced-order models (ROM) for geometrically nonlinear structures is proposed. The implicit condensation and expansion (ICE) method relies on a series of applied static loadings. From this set, a stress manifold is constructed for building the ROM. On the other hand, nonlinear normal modes rely on invariant manifold theory in order to keep the key property of invariance for the reduced subspaces. When the model coefficients are fully known, the ICE method reduces to a static condensation. However, in the framework of finite element discretisation, getting all these coefficients is generally too computationally expensive. The stress manifold is shown to tend to the invariant manifold only when a slow/fast decomposition between master and slave coordinates can be assumed. Another key problem in using the ICE method is related to the fitting procedure when a large number of modes need to be taken into account. A simplified procedure, relying on normal form theory and identification of only resonant monomial terms in the nonlinear stiffness, is proposed and contrasted with the current method. All the findings are illustrated on beams and plates examples.

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Section: Ice Methods and Stress Manifoldmentioning

confidence: 99%

Section: A Clamped-clamped Beammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reduced order models for geometrically nonlinear structures: Assessment of implicit condensation in comparison with invariant manifold approach

Shen

Béreux

Frangi

et al. 2021

European Journal of Mechanics - A/Solids

Self Cite

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“…This means that for small AC voltages, the influence of the stiffness contribution related to the equilibrium reference deflection is the highest and it determines the observed non-linear softening. As the AC voltage amplitude signal increases, consequently the effect of the vibration amplitude on the stiffness becomes the dominant one; therefore, a transition behavior from non-linear softening to hardening is reported [14][15][16].…”

Section: Experimental Results In the Non-linear Dynamic Regimementioning

confidence: 99%

Air-coupled PMUTs array with residual stresses: experimental tests in the linear and non-linear dynamic regime

Massimino

Lazarova

Quaglia

et al. 2020

International Journal of Smart and Nano Materials

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The mechanical characterization of a 4 × 4 air-coupled array of Piezoelectric Micromachined Ultrasonic Transducers (PMUTs) is presented. The experimental campaign consists of three set of experimental tests, namely: topography measurements, small signal dynamic measurements, and vibrometry in the non-linear dynamic regime. The behavior of three different kinds of PMUT are reported. They differ according to the thermo-electrical treatment that has been applied to the piezoelectric material. The presence of the fabrication induced residual stresses is investigated and the treatment effect is evaluated in terms of the initial deflected configuration. The results reported in this paper represent an experimental mechanical investigation useful for the design of PMUT structures with advanced functionalities in the linear and non-linear regime.

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“…The initial deflected configuration of the system, due to the residual stress state, is correctly captured, including the geometric non-linear effects by means of the adopted large displacements formulation. Additionally, the transducer non-linear dynamic EMA response is computed under a sinusoidal voltage input excitation at the previously estimated linearized fundamental electro-mechanical frequency f 0 [21,22,23,24]. At this stage, the linear acoustic behavior is considered for air, therefore, the non-linearities only refer to the employed large displacements formulation.…”

Section: Numerical Modelling For the Single Transducermentioning

confidence: 99%

Piezo-micro-ultrasound-transducers for air-coupled arrays: Modeling and experiments in the linear and non-linear regimes

Massimino

Colombo

Ardito

et al. 2020

Extreme Mechanics Letters

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Reduced order modelling of the non-linear stiffness in MEMS resonators

Cited by 59 publications

References 33 publications

Reduced order models for geometrically nonlinear structures: Assessment of implicit condensation in comparison with invariant manifold approach

Reduced order models for geometrically nonlinear structures: Assessment of implicit condensation in comparison with invariant manifold approach

Air-coupled PMUTs array with residual stresses: experimental tests in the linear and non-linear dynamic regime

Piezo-micro-ultrasound-transducers for air-coupled arrays: Modeling and experiments in the linear and non-linear regimes

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