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Propagation of uncertainties in the modelling of MEMS resonators (using a 3-scale probabilistic approach)
Lucas, Vincent; Wu, Ling; Golinval, Jean-Claude et al.
20151st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2015)
 

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Keywords :
Multi-scale; Stochastic
Abstract :
[en] In order to ensure the accuracy of MEMS vibrometers, the first resonance frequency should be predicted at the design phase. However, this prediction is subjected to randomness: there is a scatter in the reached value resulting from the uncertainties involved in the manufacturing process. The purpose of this work is to take into account these uncertainties of the microstructure. The objective is a non-deterministic model that can be used since the design stage. The material is the source of uncertainties: the beam resonator is made of a polycrystalline material in which each grain has a random orientation. Solving the problem with a full direct numerical simulation combined to a Monte-Carlo method allows the probability density function of the resonance frequency to be computed. However this methodology is computationally expensive due to the number of degrees of freedom required to study one sample, motivating the development of a computationally efficient method. Towards this end a 3-scales stochastic model for predicting the resonance frequency of a micro-beam made of a polycrystalline linear anisotropic material is described. At the lower scale, we model the micro-structure with micro-volume elements. Due to the small-scale involved, the representativity of these micro-volume elements is not achieved and thus Statistical Volume Elements (SVE) are considered. These SVEs are generated under the form of a Voronoï tessellation, each grain being assigned a random orientation. Computational homogenization is applied over the SVEs, along with a Monte-Carlo procedure, to obtain a stochastic characterization of the elasticity tensor at the second scale of interest, the meso-scale. The spatial correlation between SVEs is also estimated. A generator based on spectral methods is implemented. Afterwards, using a stochastic finite element method, these meso-scale uncertainties are propagated by taking account of the spatial correlation up to the higher scale to predict the probabilistic behavior of the MEMS resonator.
Disciplines :
Mechanical engineering
Materials science & engineering
Author, co-author :
Lucas, Vincent ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Wu, Ling ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Golinval, Jean-Claude  ;  Université de Liège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures
Paquay, Stéphane;  Open-Engineering S.A.
Noels, Ludovic  ;  Université de Liège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Language :
English
Title :
Propagation of uncertainties in the modelling of MEMS resonators (using a 3-scale probabilistic approach)
Publication date :
26 May 2015
Event name :
1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2015)
Event organizer :
ECCOMAS
Event place :
Crete Island, Greece
Event date :
25-27 May 2015
Audience :
International
References of the abstract :
ECCOMAS Thematic Conference - UNCECOMP 2015
Name of the research project :
3SMVIB: The research has been funded by the Walloon Region under the agreement no 1117477 (CT-INT 2011-11-14) in the context of the ERA-NET MNT framework.
Funders :
Service public de Wallonie : Direction générale opérationnelle de l'économie, de l'emploi et de la recherche - DG06
Available on ORBi :
since 01 June 2015

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