Publications

2021

• Low-Noise Synthetic Turbulence Tailored to Lateral Periodic Boundary Conditions
  
  • Rigall Tommy
  • Cotté Benjamin
  • Lafon Philippe
  Fluids, MDPI, 2021, 6 (6), pp.193. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY (10.3390/fluids)
  DOI : 10.3390/fluids
• Experimental evidence of energy transfer and vibration mitigation in a vibro-impact acoustic black hole
  
  • Li Haiqin
  • Sécail-Géraud Mathieu
  • Pelat Adrien
  • Gautier François
  • Touzé Cyril
  Applied Acoustics, Elsevier, 2021. An experimental demonstration of the broadband passive damping capacity of a vibro-impact acoustic black hole (VI-ABH) is reported. A VI-ABH is an adaptation of the classical ABH design consisting of a beam with a tapered edge of decreasing thickness creating an acoustic black hole (ABH), complemented by contact points on which the beam impacts during its vibration. The contact nonlinearity creates a rapid and efficient transfer of vibrational energy from the low-frequency range, where the ABH is known to be ineffective, to the high-frequency range, thus improving the global passive vibration mitigation characteristics. The optimal design of a VI-ABH follows the rule of locating the contact points at local maxima of the low-frequency modes. Experiments clearly demonstrate the gain in performance, both in forced and free vibrations.
• Control of the Swell by an Array of Helmholtz Resonators
  
  • Euvé Léo-Paul
  • Piesniewska Natalia
  • Maurel Agnès
  • Pham Kim
  • Petitjeans Philippe
  • Pagneux Vincent
  Crystals, MDPI, 2021, 11 (5), pp.520. We present a theoretical and experimental study of a resonator of the Helmholtz type for the control of the swell. An experimental demonstration of the shielding effect by a belt made of evenly distributed resonators is given. We then provide in-depth analysis of the Fano resonance resulting from the interference between the dock scattering (the background) and the resonant cavity scattering. This is done thanks to space–time resolved experiments which provides the complex-valued scattering coefficients and amplitude within the resonator. We provide a one-dimensional model derived in the shallow water regime owing to asymptotic analysis. The model contains the two ingredients of the Fano resonance and allows us to exhibit the damping due to leakage. When adding heuristically the damping due to losses, it reproduces the main features of the resonance observed experimentally. (10.3390/cryst11050520)
  DOI : 10.3390/cryst11050520
• Model-Based Adaptive Filtering of Dielectric Elastomer Loudspeakers
  
  • Garnell Emil
  • Doaré Olivier
  • Rouby Corinne
  , 2021. Dielectric elastomers are soft actuators that can reach deformations by more than 500% when a high voltage is applied. They have been considered for use as loudspeakers because of their quick response. One of their limitations is an inhomogeneous frequency response, due to the modal behavior of the membrane. In this study, we set up a sensor-free adaptive filtering strategy that relies on a finite element model of the loudspeaker, to improve the frequency response. (10.17743/jaes.2021.0010)
  DOI : 10.17743/jaes.2021.0010
• Particles settling dynamics
  
  • de Souza David
  , 2021. The dynamics of heavy inertial particles evolving in a fluid are of interest in many fields.They are found both in nature (water droplets in clouds, sediments in rivers and in the oceans, planetary accretion disks) and in human activities and technological applications (fuel drops in combustion chambers, chemical reactors).These systems are complex, their modelling using often strong simplifying hypotheses, and experimental data is still required in their study.A large range of behaviours can be found in such dispersed two-phase flows.This work focuses on two of these.The first is clustering, or the observation that particles accumulate in specific regions and leave others void.The second is settling velocity alteration, as particles have been observed to fall either faster or slower than in a quiescent fluid.These two phenomena are intertwined, and depend on parameters like the size and density of the particles, what the carrier phase is (water or air usually) and whether it is in a quiescent or turbulent state.An experimental device was built in which small (diameters of at most 200 µm) solid particles settle in water.Particles of various densities have been separated by size by sieving.This allows access to a large variety of particle properties.An easy to implement double-measurement technique allowing simultaneous measurements of particle and fluid velocities was developed, providing insight into particle-fluid interactions that was seldomly achieved in previous works.Increases of the settling velocity of particles falling in a quiescent fluid have been observed and could be attributed to the development of a flow that pushes the particles down.Voronoï analysis were also performed, but could not confirm with certainty whether particles formed clusters or not.This work gives interesting data, relevant in the study of particles settling in quiescent fluids in closed spaces.It also provides a reference point for future works where turbulence will be added to the system. (10.70675/36e4db36zfcefz40fczb5bcz26484f7554c8)
  DOI : 10.70675/36e4db36zfcefz40fczb5bcz26484f7554c8
• Kinked crack paths in polycarbonate samples printed by fused deposition modelling using criss-cross patterns
  
  • Corre Thomas
  • Lazarus Veronique
  International Journal of Fracture, Springer Verlag, 2021, pp.19-31. Additive manufacturing is unquestionably gaining importance in industry. Due to the layer by layer deposit process, it usually leads to an anisotropic material. A question of importance to assess their resistance to fracture is whether Linear Elastic Fracture Mechanics can be used. In this paper, we investigate this point on polycarbonate printed by Fused Deposition Modelling focusing on a criss-crossed deposit pattern. Thanks to tensile and fracture experiments instrumented by Digital Image Correlation, the material is evidenced to be linear elastic until fracture, nearly isotropic in the 2D printing plane but with a strong fracture anisotropy, leading to systematic crack kinking along the weakest plane. The Stress Intensity Factors evolution is measured across the kink and shown to be in agreement with Amestoy-Leblond's formula. The fracture toughness is observed to be larger than the bulk value, in agreement with irreversible damage and plasticity that are clearly observable at the scale of the threads. (10.1007/s10704-021-00518-x)
  DOI : 10.1007/s10704-021-00518-x
• Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures
  
  • Shen Yichang
  • Vizzaccaro Alessandra
  • Kesmia Nassim
  • Yu Ting
  • Salles Loic
  • Thomas Olivier
  • Touzé Cyril
  Vibration, MDPI, 2021, 4, pp.175 - 204. The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam). (10.3390/vibration4010014)
  DOI : 10.3390/vibration4010014
• Predicting the Type of Nonlinearity of Shallow Spherical Shells: Comparison of Direct Normal Form with Modal Derivatives
  
  • Shen Yichang
  • Kesmia Nassim
  • Touzé Cyril
  • Vizzaccaro Alessandra
  • Salles Loic
  • Thomas Olivier
  , 2021, pp.361-371. Nonlinear vibrations of free-edge shallow spherical shells with large amplitudes are investigated, with the aim of predicting the type of nonlinearity (hardening/softening behaviour) for each mode of the shell, as a function of the radius R of curvature of the shell, from the plate case (R → ∞) to the limit of non-shallow shell. Two different models (based on von Kármán's assumptions or on full numerical finite element approach), and two different methods (normal form and modal derivatives) are contrasted. (10.1007/978-3-030-81162-4_32)
  DOI : 10.1007/978-3-030-81162-4_32
• Resistivity-induced coupling between voltage distribution and vibrations in dielectric elastomers
  
  • Garnell Emil
  • Doaré Olivier
  • Rouby Corinne
  Smart Materials and Structures, IOP Publishing, 2021, 30 (2), pp.025031. (10.1088/1361-665X/abd58f)
  DOI : 10.1088/1361-665X/abd58f
• 1D/3D Finite-Volume coupling in conjunction with beam/shell elements coupling for fast transients in pipelines with fluid–structure interaction
  
  • Daude Frédéric
  • Galon P.
  • Douillet-Grellier T.
  Journal of Fluids and Structures, Elsevier, 2021, 101, pp.103219. (10.1016/j.jfluidstructs.2021.103219)
  DOI : 10.1016/j.jfluidstructs.2021.103219
• A hyperbolic phase-transition model coupled to tabulated EoS for two-phase flows in fast depressurizations
  
  • de Lorenzo M.
  • Lafon Ph.
  • Pelanti M.
  • Pantano A.
  • Di Matteo M.
  • Bartosiewicz Y.
  • Seynhaeve J.-M.
  Nuclear Engineering and Design, Elsevier, 2021, 371, pp.110954. (10.1016/j.nucengdes.2020.110954)
  DOI : 10.1016/j.nucengdes.2020.110954
• RESOLUTION OF FLUID-STRUCTURE COUPLED PROBLEMS WITH FLOW USING THE BOUNDARY ELEMENT METHOD
  
  • Le Mestre Robin
  • Schotté Jean-Sébastien
  • Doaré Olivier
  , 2021. Effects of fluid-structure coupling on the dynamic behaviour of flexible airship can be modelled with a potential, incompressible, inviscid flow. A new formalism to study linear variations of the flow induced on the fluid-structure interface in a time dependent ambient flow is introduced. The features of the Boundary Element Method used to solve this problem numerically are exhibited. Numerical results of the linear model are compared with analytical and non linear numerical results, assessing the validity and the limitations of the approach.
• Scattering of acoustic waves by a nonlinear resonant bubbly screen
  
  • Pham Kim
  • Mercier Jean-François
  • Fuster Daniel
  • Marigo Jean-Jacques
  • Maurel Agnès
  Journal of Fluid Mechanics, Cambridge University Press (CUP), 2021, 906, pp.A19. Some of the authors of this publication are also working on these related projects: PARIS code View project Homogenization of thin and thick microstructured materials View project (10.1017/jfm.2020.799)
  DOI : 10.1017/jfm.2020.799
• Scattering of acoustic waves by a nonlinear resonant bubbly screen
  
  • Pham Kim
  • Mercier Jean-Francois
  • Fuster Daniel
  • Marigo Jean-Jacques
  • Maurel Agnès
  Journal of Fluid Mechanics, Cambridge University Press (CUP), 2021, 906, pp.A19. Abstract (10.1017/jfm.2020.799)
  DOI : 10.1017/jfm.2020.799
• Variational modelling of nematic elastomer foundations
  
  • Cesana Pierluigi
  • Baldelli Andrés A. León
  , 2021. We compute the $\Gamma$-limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic membrane. We work in the regime of infinitesimal displacements and model the orientation of the liquid crystal according to the order tensor theories of both Frank and De Gennes. We describe the asymptotic regime by analysing a family of functionals parametrised by the thickness of the membranes and the relative ratio of the elastic constants, establishing that, in the limit, the system is represented by a two-dimensional integral functional interpreted as a linear membrane on top of a nematic active foundation involving an effective De Gennes optic tensor which allows for low order states. The latter can suppress shear energy by formation of microstructure as well as act as a pre-strain transmitted by the foundation to the overlying film.
• Gamma-convergence results for nematic elastomer bilayers: relaxation and actuation
  
  • Cesana Pierluigi
  • León Baldelli Andrés
  , 2021. We compute effective energies of thin bilayer structures composed by soft nematic elastic-liquid crystals in various geometrical regimes and functional configurations. Our focus is on order-strain interaction in elastic foundations composed of an isotropic layer attached to a nematic substrate. We compute Gamma-limits as the layers thickness vanishes in two main scaling regimes exhibiting spontaneous stress relaxation and shape-morphing, allowing in both cases out-of-plane displacements. This extends the plane strain modelling of [*], showing the asymptotic emergence of fully coupled macroscopic active-nematic foundations. Subsequently, we focus on actuation and compute asymptotic configurations of an active plate on nematic foundation interacting with an applied electric field. From the analytical standpoint, the presence of an electric field and its associated electrostatic work turns the total energy into a non-convex and non-coercive functional. We show that equilibrium solutions are min-max points of the system, that min-maximising sequences pass to the limit and, that the limit system can exert mechanical work under applied electric fields. [*]: P. Cesana and A. A. Le\'on Baldelli. "Variational modelling of nematic elastomer foundations". In: Mathematical Models and Methods in Applied Sciences 14 (2018)
• Role of particle aggregation on the structure of dried colloidal silica layers
  
  • Lesaine Arnaud
  • Bonamy Daniel
  • Rountree Cindy Lynn
  • Gauthier Georges
  • Impéror-Clerc Marianne
  • Lazarus Veronique
  Soft Matter, Royal Society of Chemistry, 2021, 17, pp.1589. The process of colloidal drying gives way to particle self-assembly in numerous elds including photonics or biotechnology. Yet, the mechanisms and conditions driving the nal particle arrangement in dry colloidal layers remain elusive. Here, we examine how the drying rate selects the nanostructure of thick dried layers in four dierent suspensions of silica nanospheres. Depending on particle size and dispersity, either an amorphous arrangement, a crystalline arrangement, or a rate-dependent amorphous-to-crystalline transition occurs at the drying surface. Amorphous arrangements are observed in the two most polydisperse suspensions while crystallinity occurs when dispersity is lower. Counter-intuitively in the latter case, a higher drying rate favors ordering of the particles. To complement these measurements and to take stock of the bulk properties of the layer, tests on the layer porosity were undertaken. For all suspensions studied herein, faster drying yields denser dry layers. Crystalline surface arrangement implies large bulk volume fraction (∼ 0.65) whereas amorphous arrangements can be observed in layers with either low (down to ∼ 0.53) or high (∼ 0.65) volume fraction. Lastly, we demonstrate via targeted additional experiments and SAXS measurements, that the packing structure of the layers is mainly driven by the formation of aggregates and their subsequent packing, and not by the competition between Brownian diusion and convection. This highlights that a second dimensionless ratio in addition to the Peclet number should be taken into account, namely the aggregation over evaporation timescale. (10.1039/D0SM00723D)
  DOI : 10.1039/D0SM00723D
• Revisiting imperfect interface laws for two-dimensional elastodynamics
  
  • Pham Kim
  • Maurel Agnès
  • Marigo Jean-Jacques
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, 2021, 477 (2245), pp.20200519. We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition effective parameters provided by static, elementary problems being the equivalents of the cell problems in classical two-scale homogenization. The derivation of the model is conducted in the transient regime and its stability is guarantied by the positiveness of the effective interfacial energy. Spring models are envisioned as particular cases. It is shown that massless-spring models are recovered in the limit of small void thicknesses and collinear cracks. By contrast, the use of mass-spring model is justified at normal incidence, otherwise unjustified. We provide quantitative validations of our model and comparison with spring models by means of comparison with direct numerical calculations in the harmonic regime. (10.1098/rspa.2020.0519)
  DOI : 10.1098/rspa.2020.0519
• Numerical bifurcation and stability analysis of variational gradient-damage models for phase-field fracture
  
  • León Baldelli Andrés A
  • Maurini Corrado
  Journal of the Mechanics and Physics of Solids, Elsevier, 2021, 152 (104424), pp.104424. Gradient damage models used in phase-field approaches to brittle fracture are characterised by material softening and instabilities. We present novel numerical techniques for the bifurcation and stability analysis along quasi-static evolution paths as well as practical tools to select stable evolutions. Our approach stems from the variational approach to fracture and the theory of rate-independent irreversible processes whereby a quasi-static evolution is formulated in terms of incremental energy minimisation under unilateral constraints. Focussing on the discrete setting obtained with finite elements techniques, we discuss the links between bifurcation criteria for an evolution and stability of equilibrium states. Key concepts are presented through the analytical solution of a two-degreesof-freedom model featuring a continuum family of bifurcation branches. We introduce numerical methods to i) assess (second-order) stability conditions for time-discrete evolutions subject to damage irreversibility, and ii) to select possible stable evolutions based on an energetic criterion. Our approach is based on the solution of a coupled eigenvalue problem which accounts for the time-discrete irreversibility constraint on damage. Several numerical examples illustrate that this approach allows us to filter out unstable solutions provided by standard (first-order) minimisation algorithms as well as to effectively compute stable evolution paths. We demonstrate our purpose on a multifissuration problem featuring complex fracture patterns, to show how the eigenvalue analysis enables to compute and retrieve morphological properties of emerging cracks. (10.1016/j.jmps.2021.104424)
  DOI : 10.1016/j.jmps.2021.104424
• Adaptation of the nuclear safety code CATHARE3 to supercritical helium flow
  
  • Shoala Sulayman
  • Hoa Christine
  • Ercolani Eric
  • Poncet Jean-Marc
  • Le Thanh Kim-Claire
  • Dupouy François
  • Vallcorba Roser
  • Lacroix Benoit
  • Nicollet Sylvie
  Cryogenics, Elsevier, 2021, 113. Several international projects on nuclear fusion are in progress and comprise cryogenic systems for cooling components such as superconducting magnets. Different thermal-hydraulic codes already exist for sizing and validating these cryogenic devices. However, there is still no qualified scientific calculation tool to perform safety thermal hydraulic analyses encountered in fusion reactors. For this purpose, we have started the adaptation of the CATHARE system code, the reference thermal-hydraulic tool for safety studies of French Pressurised Water Reactors developed by CEA, EDF, Framatome, and IRSN, to model supercritical helium flows. Properties of supercritical helium were already available in CATHARE with the fluid library REFPROP. We implemented suitable correlations for friction factors and heat transfer coefficients to account for specific hydraulic parameters of helium flow in Cable In Conduit Conductors (CICC) that are used in superconducting magnets. Then, we performed first evaluations of the CATHARE code abilities to model thermal-hydraulic transient in cryogenic devices of a tokamak. Two cases of helium flow in a CICC of a JT-60SA toroidal field coil have been studied, and comparisons were performed with experimental data and the THEA code developed by CryoSoft. Simulations focusing on the behaviour of a device protected by a safety valve against incidental pressure increase were also performed. CATHARE results were compared with available experimental data on supercritical helium discharge through the safety valve of a tank in case of failure of the insulating vacuum. (10.1016/j.cryogenics.2020.103135)
  DOI : 10.1016/j.cryogenics.2020.103135
• Linear and nonlinear dynamics of a plate with acoustic black hole, geometric and contact nonlinearity for vibration mitigation
  
  • Li Haiqin
  • Touzé Cyril
  • Gautier François
  • Pelat Adrien
  Journal of Sound and Vibration, Elsevier, 2021. A rectangular plate with a wedge profile creating an Acoustic Black Hole (ABH) termination is studied numerically. A particular emphasis is put on combining two different types of nonlinearity in order to improve the passive damping capacity of the ABH by transferring energy to the high-frequency range where it is more efficient. First, the addition of contact points to create a vibro-impact black hole (VI-ABH) is taken into account, following a previous study on beams. The contact nonlinearity allows for a rapid and efficient transfer of energy. Second, the large-amplitude vibrations of the plate in the ABH region where small thickness is reached, is also considered. The geometric nonlinearity is incorporated using a von Kármán plate model, and the regime of wave turbulence is shown to be triggered thus creating an energy flux from the low to the high frequencies. The linear characteristics of the ABH plate are first analyzed. Numerical results show the appearance of overdamped modes gathered in solution branches with constant number of half-waves in the transverse direction of the ABH, seen as a waveguide. The structure of the branches is shown to be more and more prominent when increasing the width of the plate, showing a transition from beam-like to full plate structure, with a fixed value for the fundamental cut-on frequency. The combination of both contact and geometric nonlinearities to improve the ABH effect is then reported. It is shown that the coexistence of both nonlinearities provides better passive damping efficacy. (10.1016/j.jsv.2021.116206)
  DOI : 10.1016/j.jsv.2021.116206
• Research on the impacts of wind turbine noise on humans: sound, perception, health (RIBEolH)
  
  • Evrard Anne Sophie
  • Avan Paul
  • Champelovier Patricia
  • Cotté Benjamin
  • Ecotiere David
  • Gauvreau Benoit
  • Giorgis-Allemand L
  • Marquis-Favre Catherine
  • Meunier Sabine
  , 2021. Wind energy is expanding rapidly in France as elsewhere in the world, but the population is worried about the health impacts of wind turbine noise and some people are more annoyed than the sound field measurements would suggest. The annoyance is often described as resulting from infrasounds (IS) whereas the acoustic pressures of IS emitted by wind turbines would be below the perception thresholds. However, the possible inaudibility of IS does not exclude their action on the inner ear or the central nervous system (CNS). In this context, we propose a Research project on the Impacts of wind turbine noise on humans, in terms of sound simulation/synthesis and perception, and its effects on human Health (“RIBEolH”). The objectives of RIBEolH project are: - To assess the health effects of audible noise, low-frequency sounds (LFS) particularly, and IS, emitted by wind turbines. - To better understand the auditory mechanisms associated with the perception of IS and LFS emitted by wind turbines. - To better understand the effects of IS on the inner ear or CNS. To address these objectives, RIBEolH is based on two complementary parts: an epidemiological study and a psychoacoustic and physiological study.
• Frequency and Amplitude Modulations of a Moving Structure in Unsteady Non-Homogeneous Density Fluid Flow
  
  • Rajaomazava Tolotra Emerry
  • Benaouicha Mustapha
  • Astolfi Jacques-André
  • Boudraa Abdel-Ouahab
  Fluids, MDPI, 2021, 6 (3), pp.130. A fluid-structure interaction’s effects on the dynamics of a hydrofoil immersed in a fluid flow of non-homogeneous density is presented and analyzed. A linearized model is applied to solve the fluid-structure coupled problem. Fluid density variations along the hydrofoil upper surface, based on the sinusoidal cavity oscillations, are used. It is shown that for the steady cavity case, the value of cavity length Lp does not affect the amplitude of the hydrofoil displacements. However, the natural frequency of the structure increases according to Lp. In the unsteady cavity case, the variations of the added mass and added damping (induced by the fluid density rate of change) generate frequency and amplitude modulations in the hydrofoil dynamics. To analyse this phenomena, the empirical mode decomposition, a well established data-driven method to handle such modulations, is used. (10.3390/fluids6030130)
  DOI : 10.3390/fluids6030130
• Backbone curves, Neimark-Sacker boundaries and appearance of quasi-periodicity in nonlinear oscillators: application to 1:2 internal resonance and frequency combs in MEMS
  
  • Gobat Giorgio
  • Guillot Louis
  • Frangi Attilio
  • Cochelin Bruno
  • Touzé Cyril
  Meccanica, Springer Verlag, 2021, 56, pp.1937-1969. 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. (10.1007/s11012-021-01351-1)
  DOI : 10.1007/s11012-021-01351-1
• Reduced order modelling and experimental validation of a MEMS gyroscope test-structure exhibiting 1:2 internal resonance
  
  • Gobat Giorgio
  • Zega Valentina
  • Fedeli Patrick
  • Guerinoni Luca
  • Touzé Cyril
  • Frangi Attilio
  Scientific Reports, Nature Publishing Group, 2021, 11, pp.16390. 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. (10.1038/s41598-021-95793-y)
  DOI : 10.1038/s41598-021-95793-y