Publications

2022

• Physics-based synthesis of wind turbine noise
  
  • Mascarenhas David
  , 2022. It is known that the wind turbine noise is a potential source of disturbance and annoyance for the people in the vicinity of the wind farms. The work presented in the thesis addressed the problem of wind turbine noise by developing a physic-based model to synthesize and study it. The synthesis model detailed here advances from the frequency-domain model for wind turbine noise developed by Tian and Cotté and revisits certain components in light of the recent literature. A synthesis tool is created to convert the frequency domain noise predictions to a time signal with the help of a window function. The designed window function is made to account for the difference in the propagation time observed due to the rotation of the blades.A few test cases of the synthesized sound can be found in the thesis for different scenarios. The model is finally compared to the field measurements done for an entire wind farm and show fairly good results for the source as well as the propagation part. The developed model is a useful tool which can be used for psychoacoutic evaluation to understand the perception and annoyance factor of wind turbine noise. Along with obtaining the spectral levels of the expected noise from the wind farm, the tool also produces audible signals that can be further used for the desired purpose. Thus making it a useful tool that abridges the gap between citizens, local authorities and acousticians. (10.70675/e0fc954azd27ez4cdazba62z449f919f798f)
  DOI : 10.70675/e0fc954azd27ez4cdazba62z449f919f798f
• Experimental analysis and modeling of porous NiTi shape memory alloys
  
  • Özeri̇m Beki̇loğlu Gülcan
  , 2022. Experiments show that porosity brings new features to NiTi shape memory alloys such as low stiffness and density. The bio-compatible porous NiTi, especially with the pseudoelastic behavior, has a great potential for implant applications in the human body. Although different techniques are provided in the literature for manufacturing NiTi samples, the subject is still open for further investigation to achieve superior shape memory characteristics from the material. Based on this, the aim of the PhD thesis is to analyze and model the mechanical behavior of porous NiTi shape memory alloys.Porous NiTi compacts were produced using spark plasma sintering (SPS), and tested under uniaxial compression to observe the pseudoelasticity and shape memory effect. After sintering, the samples did not show the expected pseudoelastic behavior, and they were subjected to further heat treatment and characterization. A wide range of homogenization and/or aging were applied at different temperatures and duration, and the effect of heat treatment on the pseudoelastic behavior of SPSed NiTi was investigated systematically. Transformation behavior was observed using differential scanningcalorimetry, and phase composition was identified using X-ray diffraction (XRD). These characterizations gave an insight into the micro-structure of the SPSed samples after heat treatment. Then the mechanical behavior of the samples was studied. Instrumented micro-indentation was carried out to measure the hardness altered by aging. Selected samples were tested under uniaxial compression and differences in their pseudoelastic behavior were shown on stress-strain diagrams. At the end, an enhancement in the pseudoelastic response of the SPSed NiTi samples was observed, and the effect ofheat-treatment was discussed.In the modeling part, a macro-scale phenomenological model was proposed for the mechanical behavior of porous SMAs by using a poromechanics approach. The new phenomenological model considers the porous medium as a skeleton consisting of a solid matrix and connected porous space. The model was built starting from a dense SMA model (Zaki-Moumni model) in which the porosity was included as an internal state variable. Both the pseudoelastic and plastic deformations were considered, and the model was implemented into Abaqus through a user-defined material subroutine (UMAT) by using the implicit backward-Euler integration scheme. The phenomenological model was validated using experimental results available in the literature, and the numerical results obtained from the unit cell (UC) technique used in this study. The uni-axial stress-strain response was captured to a great extent with a significant reduction in numerical cost when compared to the UC approach. It isshown that the proposed model represents the mechanical behavior of porous SMAs with reasonable accuracy and could be especially useful in possible biomedical applications of SMAs. (10.70675/674fdfe8zb640z4b90z9968zbbaa010fe56f)
  DOI : 10.70675/674fdfe8zb640z4b90z9968zbbaa010fe56f
• High order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to generic forcing terms and parametrically excited systems
  
  • Opreni Andrea
  • Vizzaccaro Alessandra
  • Touzé Cyril
  • Frangi Attilio
  Nonlinear Dynamics, Springer Verlag, 2022, 110 (6), pp.5401-5447. The direct parametrisation method for invariant manifolds is used for model order reduction of forced-damped mechanical structures subjected to geometric nonlinearities. Nonlinear mappings are introduced, allowing one to pass from the degrees of freedom of the finite-element model to the normal coordinates. Arbitrary order of expansions are considered for the unknown mappings and the reduced dynamics, which are then solved sequentially through the homological equations, for both autonomous and time-dependent terms. It is emphasized that the two problems share a similar structure, which can be used for an efficient implementation of the non-autonomous added terms. A special emphasis is also put on the new resonance conditions arising due to the presence of the external forcing frequencies, which allows predicting phenomena such as parametric excitation and isolas formation. The method is then applied to structures of academic and industrial interest. First, the large amplitude vibrations of a forceddamped cantilever beam are studied. This example highlights that high order non-autonomous terms are compulsory to correctly estimate the maximum vibration amplitude experienced by the structure. The birth of isolated solutions is also illustrated on this example. The cantilever is then used to show how quadratic coupling creates conditions for the excitation of the parametric instability, all these features being correctly embedded in the reduction process. A shallow arch excited with multi-modal forcing is then studied to detail different forcing effects. Finally, the approach is validated on a structure of industrial relevance, i.e. a comb driven micro-electro-mechanical resonator. The accuracy and computational performance reported suggest that the proposed methodology can accurately predict the nonlinear dynamic response of a large class of nonlinear vibratory systems. (10.1007/s11071-022-07978-3)
  DOI : 10.1007/s11071-022-07978-3
• Drag coefficient Uncertainty for floating wind turbines
  
  • Robaux Fabien
  • Nadal Adria Borras
  • Peyrard Christophe
  • Benoit Michel
  • Benguigui William
  • Guiton Martin
  , 2022.
• Modèles mécaniques de poutre enrichis pour la simulation de tubes minces sous pression
  
  • Pascal-Abdellaoui Youri
  , 2022. Le phénomène de fouettement est une des conséquences potentielles de la rupture accidentelle d'une tuyauterie haute énergie (RTHE). Le fouettement doit être pris en compte dans les études sur la sûreté des installations industrielles puisqu'il suppose de grands déplacements de la tuyauterie sectionnée qui pourrait, en fonction de l'encombrement, impacter les structures et composants avoisinants. S'agissant de phénomènes physiques complexes, la caractérisation de la rupture de la tuyauterie et du fouettement associé est fondée actuellement sur des approches simplifiées reposant sur des hypothèses conservatives. Ces hypothèses peuvent alors conduire à des difficultés, ce qui est résolu par l'introduction de modifications au niveau de ces installations, modifications qui peuvent s'avérer coûteuses. De façon à répondre à ces enjeux, il est proposé dans ce projet de recherche un travail d'amélioration des outils et méthodes actuellement disponibles pour la simulation du phénomène de fouettement afin de rendre plus réaliste la modélisation des phénomènes physiques prépondérants et en particulier leur couplage. Pour cela, il est nécessaire de prendre en compte dans la modélisation un grand nombre de phénomènes. Il s'agit, en particulier, de modéliser les évènements suivants : la rupture de la tuyauterie, la force du jet initié à la brèche, le déplacement de la tuyauterie sectionnée, l'impact de celle-ci avec les structures avoisinantes, les déformations plastiques suite à cet impact et la formation éventuelle d'une rotule plastique ainsi que l'interaction entre le fluide contenu dans la tuyauterie et la structure. De nombreuses études ont été réalisées en modélisation tridimensionnelle, laquelle s'avère coûteuse en temps de calcul et de simulation. Il est donc souhaité de modéliser de façon simplifiée la dynamique de la tuyauterie rompue afin de permettre une évaluation rapide des conditions de sûreté. Il a en particulier été montré, qu'en l'état actuel des modélisations, il était nécessaire de modéliser la zone d'impact de la tuyauterie en éléments coques non-linéaires pour retrouver une estimation correcte de la force d'impact de la tuyauterie sur l'obstacle. Ainsi un élément fini de type poutre enrichi permettant de prendre en considération l'ovalisation de sa section transverse est développé, que ce soit sur une poutre droite ou sur une poutre ayant une courbure initiale comme dans le cas d'un coude. La cinématique retenue est une cinématique classique de poutre d'Euler-Bernoulli à laquelle s'ajoute une cinématique de coque de type Love-Kirchhoff, développée au premier ordre dans l'épaisseur du tube et en séries de Fourier selon la variable tangentielle afin de rester dans un formalisme filaire. De plus un couplage non linéaire, entre les rotations de type poutre et les déplacements de la section de type coque, est introduit afin de permettre au tube de s'ovaliser même sur une partie droite. Le modèle décrit est alors discrétisé et implémenté dans le code de calcul industriel de dynamique rapide explicite Europlexus. Afin de vérifier et de valider le modèle, la tuyauterie est soumise à différents cas de chargement tels que l'extension simple, la flexion pure, le tube sous pression interne ou encore l'application d'une force surfacique localisée sur la section transverse permettant de grandes déformations de la section. Les résultats numériques obtenus sont en bonne adéquation avec les solutions analytiques ou numériques issues d'autres codes industriels. (10.70675/6340f1eazb5b1z4642za9caz2761b6009b81)
  DOI : 10.70675/6340f1eazb5b1z4642za9caz2761b6009b81
• Diffraction grating with space-time modulation
  
  • Pham Kim
  • Maurel Agnès
  Journal of Computational Physics, Elsevier, 2022, 469, pp.111528. We present a theoretical and numerical analysis of the diffraction of acoustic waves by space-time modulated gratings with rigid-type modulations. This is done by deriving the form of the modes which are exact, uncoupled, solutions of the problem in the unbounded regions, inside and outside the grating. The dispersion of the modes is studied as a function of the ratio of the modulation speed to the speed of sound which shows that each spatial diffraction order is associated with a single temporal diffraction order. For a grating of finite extend, the solution is obtained as a superposition of these modes, which couple at the grating interfaces. This provides a numerical, multimodal, method when considering a truncated version of the solution. We provide analysis of the solutions in the harmonic and in the transient regimes. (10.1016/j.jcp.2022.111528)
  DOI : 10.1016/j.jcp.2022.111528
• Frequency combs in a MEMS resonator featuring 1:2 internal resonance: ab initio reduced order modelling and experimental validation
  
  • Gobat Giorgio
  • Zega Valentina
  • Fedeli Patrick
  • Touzé Cyril
  • Frangi Attilio
  Nonlinear Dynamics, Springer Verlag, 2022. Abstract This paper is devoted to a detailed analysis of the appearance of frequency combs in the dynamics of a micro-electro-mechanical systems (MEMS) resonator featuring 1:2 internal resonance. To that purpose, both experiments and numerical predictions are reported and analysed to predict and follow the appearance of the phononic frequency comb arising as a quasi-periodic regime between two Neimark-Sacker bifurcations. Numerical predictions are based on a reduced-order model built thanks to an implicit condensation method, where both mechanical nonlinearities and electrostatic forces are taken into account. The reduced order model is able to predict a priori, i.e. without the need of experimental calibration of parameters, and in real time, i.e. by solving one or two degrees-of-freedom system of equations, the nonlinear behaviour of the MEMS resonator. Numerical predictions show a good agreement with experiments under different operating conditions, thus proving the great potentiality of the proposed simulation tool. In particular, the bifurcation points and frequency content of the frequency comb are carefully predicted by the model, and the main features of the periodic and quasi-periodic regimes are given with accuracy, underlining that the complex dynamics of such MEMS device is effectively driven by the characteristics of the 1:2 internal resonance. (10.1007/s11071-022-08029-7)
  DOI : 10.1007/s11071-022-08029-7
• Auralization of wind turbine noise using physics-based emission and propagation models
  
  • Mascarenhas David
  • Cotté Benjamin
  • Doaré Olivier
  , 2022, Proceedings of the 24th International Congress on Acoustics (ICA 2022).
• Nouvelles approches numériques pour la modélisation des massifs rocheux dégradés. Application au creusement des ouvrages souterrains soutenus.
  
  • Defay Angeline
  , 2022. Les massifs rocheux dégradés sont de plus en plus rencontrés dans les projets d'aménagement car les contraintes (environnementales, foncières…) amènent à conduire des projets dans ces terrains géologiquement défavorables. L’état de l’art très insatisfaisant de l’ingénierie rocheuse pour ce type de terrains induit des écarts importants entre les calculs et le comportement réel. Dans le domaine des tunnels, la méthode classique (convergence-confinement) donne des résultats incertains pour ce type de terrain et n’a plus été actualisée depuis une quinzaine d’années, et les différentes formulations utilisées pour améliorer les résultats atteignent leurs limites, n'ayant pas été établies pour les roches.L'objectif de cette thèse est de développer les outils permettant de modéliser de manière plus réaliste le comportement des massifs rocheux. Ce comportement est représenté par le critère de Hoek et Brown régularisé dans le plan déviatorique, qui prend en compte l'effet de la contrainte principale intermédiaire et de l'angle de Lode. Les développements théoriques ont été construits dans l'espace des contraintes représenté par la trisectrice et le plan déviatorique, qui permet le calcul des déformations plastiques selon la projection orthogonale, ou en intégrant un angle de dilatance fixé. Ces développements sont ensuite utilisés pour la modélisation d'un tunnel soutenu en milieux rocheux, en utilisant un algorithme stationnaire. Les résultats des modélisations ont permis d'établir la validité de la méthode convergence-confinement et de nouvelles formules pour les massifs dégradés. (10.70675/c3aae2c5z2590z4563za2d7z6ef89f0f2f40)
  DOI : 10.70675/c3aae2c5z2590z4563za2d7z6ef89f0f2f40
• L-PBF and DED processing of a Ni-based superalloy
  
  • Thomas M
  • Charkaluk Eric
  • Solas Denis
  • Szmytka Fabien
  • Locq Didier
  • Morel Ariel
  • Hubert Olivier
  • Muller Nicolas
  • Tournier Christophe
  , 2022. Different additive manufacturing (AM) technologies such as L-PBF and DED do become really attractive for both repair and 3D part manufacturing. In particular, extensive work is in progress for the non-weldable nickel-based superalloys which tend to exhibit cracks due to residual stresses build-up during AM thermal cycles. Within the framework of the project FAPS conducted at Université Paris-Saclay, the present investigation will highlight the processing conditions and build-up strategy that produce crack-free specimens for alloy AD730®. The latter was developed by Aubert & Duval for cast&wrought gas turbine applications. In this work, a comparison between such conventional processing and AM will be provided in terms of mechanical performance. The results clearly show an anisotropic behaviour related to the sharp crystallographic texture induced by the epitaxial grain growth. The results will be discussed, with a perspective analysis of maturity for this AM processedmaterial, the process robustness, the potential technological developments and application prospects.
• Experimental study of the dynamic stall noise on an oscillating airfoil
  
  • Raus David
  • Cotté Benjamin
  • Monchaux Romain
  • Jondeau Emmanuel
  • Souchotte Pascal
  • Roger Michel
  Journal of Sound and Vibration, Elsevier, 2022, 537, pp.117144. (10.1016/j.jsv.2022.117144)
  DOI : 10.1016/j.jsv.2022.117144
• Improving mechanical characteristics of a Zr based metallic glass under dynamic conditions by dynamic predeformation
  
  • Bayard Marine
  • Blétry Marc
  • Héripré Eva
  • Maitournam Habibou
  Materials Letters, Elsevier, 2022, 330, pp.133219. The effects of dynamic predeformation on the dynamic behaviour of metallic glasses (MG) are investigated through split Hopkinson pressure bar (SHPB) tests. The results obtained on samples fractured in a single test are compared with those on samples fractured in two successive SHPB tests. They show a reduction in data scatter and an increase in maximum stress for predeformed samples. (10.1016/j.matlet.2022.133219)
  DOI : 10.1016/j.matlet.2022.133219
• Seismic analysis of tall buildings through an enriched equivalent beam model: Application to Grenoble City Hall
  
  • Franco Ariza Graciela Carolina
  • Chesnais Céline
  • Semblat Jean-François
  • Desprez Cédric
  • Cédric Giry
  , 2022. The seismic assessment of multi-story buildings at city scale requires robust but simplified modeling techniques to reduce the computational resources and time. This paper presents an equivalent beam model (EBM), issued from homogenization, capable of describing the seismic response of real tall buildings. The EBM is a generalization of the Timoshenko beam model. It integrates shear, global bending, and inner bending mechanisms, which are identified to control the response of reticulated structures such as buildings, foams, honeycombs, or lattice structures. The parameters of the EBM are obtained through the static analysis of a single building story. This work uses a new finite element formulation of the EBM to estimate the dynamic properties of buildings (i.e., eigenfrequencies and eigenmodes) and perform time history analyses with natural seismic records. This approach is validated through a real case study. The Grenoble City Hall corresponds to a regular 13-story reinforced concrete building located in Grenoble-France. The inner bending significantly influences its behavior, whereas usual beam models do not include this mechanism. The results obtained via this 1D simplified EBM match those obtained with a fully 3D finite element simulation, which are also very close to experimental data.
• Kinematic interaction forces in rigid inclusions under seismic loading
  
  • Shen Yuxiang
  • Pérez-Herreros Jesús
  • Cuira Fahd
  • Semblat Jean-François
  • Burlon Sébastien
  , 2022, pp.172-179. The reinforcement technique with rigid inclusions is considered as a practical, economical, and time-saving foundation solution. Several studies have recently focused on the static and cyclic behaviour of this reinforced foundation system. However, its seismic behaviour has not yet been widely studied. This paper presents a state of the art in the dynamic soil-structure interaction studies on foundation reinforced with rigid inclusions. Special attention is given to the estimation of the kinematic bending moments of inclusions in different soil deposits comprising several stiffness contrasts. The kinematic bending moments calculated by a transient dynamic analysis are compared with those obtained by means of pseudo-static Winkler model approach. The results show that, compared to the dynamic approach, the pseudo-static approach is able to predict the location where the maximum bending moment develops but underestimates its amplitude for important values of the stiffness contrast at the corresponding interface between soil layers.
• Étude de l’acier inoxydable super-duplex 2507 fabriqué par procédé DED : de la fabricabilité à la caractérisation
  
  • Ballésio Sébastien
  • Le Hong Thai
  • Comas Chloé
  • Dhondt Matthieu
  • Doudard Cédric
  • Szmytka Fabien
  , 2022.
• Analyse des effets de taille : Comparaison entre le modèle TLS (Thick Level Set) et le Critère Couplé
  
  • Zghal Jihed
  • Moes Nicolas
  • Leguillon Dominique
  • Stolz Claude
  , 2022. La prédiction de la charge critique d’une structure présentant un défaut reste à ce jour un grand challenge. Dans cette étude, nous proposons de mettre en évidence la nocivité d’une entaille aigüe en V à travers une étude comparative de la contrainte à la rupture obtenue par le modèle TLS et par le critère couplé. En effet, la nocivité de l’entaille est plus importante quand sa taille est supérieure à la longueur caractéristique du matériau. Nous avons montré que les prédictions de la contrainte à la rupture par le critère couplé sont surestimées quand la taille de l’entaille devient plus petite par rapport à la longueur caractéristique du matériau.
• Wind turbine noise modeling including aeroacoustic sources and propagation effects: comparison against field measurements
  
  • Mascarenhas David
  • Cotté Benjamin
  • Doaré Olivier
  • Ecotiere David
  • Guillaume Gwenaël
  • Gauvreau Benoit
  • Schmich-Yamane Isabelle
  • Junker Fabrice
  , 2022. The study of wind turbine noise and its impact is of growing importance with the increase in the demand for green and clean energy. As it is known that wind turbine noise can be a cause of annoyance in the vicinity of wind farms it is beneficial to predict with certain accuracy the generated noise in the design phase itself. A crucial step is the validation of prediction models against field measurements (in-situ). This article presents a wind turbine noise prediction model that combines Amiet’s theory to calculate trailing edge noise and turbulence interaction noise in free field with a wide-angle parabolic equation valid in moving media to account for the long-range acoustic propagation effects. The model considers the wind turbine as an extended noise source and the rotation effects (such as the convective amplification and Doppler effect) are taken into account. The predicted noise levels are compared to those obtained from a measurement campaign where acoustic, meteorological and ground impedance data have been recorded simultaneously. First, the sound source model is validated close to the wind turbines for different wind speeds and directions. Then, noise predictions are compared to SPL measurements at various distances from the sound source, between 350 and 1300 meters.
• Arbitrary-rate relaxation techniques for the numerical modeling of compressible two-phase flows with heat and mass transfer
  
  • Pelanti Marica
  International Journal of Multiphase Flow, Elsevier, 2022, 153, pp.104097. (10.1016/j.ijmultiphaseflow.2022.104097)
  DOI : 10.1016/j.ijmultiphaseflow.2022.104097
• Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effect
  
  • Shami Zein Alabidin
  • Shen Yichang
  • Giraud-Audine Christophe
  • Touzé Cyril
  • Thomas Olivier
  Meccanica, Springer Verlag, 2022. This article considers the nonlinear dynamics of coupled oscillators featuring strong coupling in 1:2 internal resonance. In forced oscillations, this particular interaction is the source of energy exchange, leading to a particular shape of the response curves, as well as quasi-periodic responses and a saturation phenomenon. These main features are embedded in the simplest system which considers only the two resonant quadratic monomials conveying the 1:2 internal resonance, since they are the proeminent source allowing one to explain these phenomena. However, it has been shown recently that those features can be substantially modified by the presence of non-resonant quadratic terms. The aim of the present study is thus to explain the effect of the non-resonant quadratic terms on the dynamics. To that purpose, the normal form up to the third order is used, since the effect of the non-resonant quadratic terms will be transferred into the resonant cubic terms. Analytical solutions are detailed using a second-order mutliple scale expansion. A thorough investigation of the backbone curves, their stability and bifurcation, and the link to the forced–damped solutions, is detailed, showing in particular interesting features that had not been addressed in earlier studies. Finally, the saturation effect is investigated, and it is shown how to correct the detuning effect of the cubic terms thanks to a specific tuning of non-resonant quadratic terms and resonant cubic terms. This choice, derived analytically, is shown to extend the validity of the saturation effect to larger amplitudes, which can thus be used in all applications where this effect is needed e.g. for control. (10.1007/s11012-022-01566-w)
  DOI : 10.1007/s11012-022-01566-w
• Liquefaction assessment of silty sands: Experimental characterization and numerical calibration
  
  • Gobbi Stefania
  • Santisi D’avila Maria Paola
  • Lenti Luca
  • Semblat Jean-François
  • Reiffsteck Philippe
  Soil Dynamics and Earthquake Engineering, Elsevier, 2022, 159, pp.107349. (10.1016/j.soildyn.2022.107349)
  DOI : 10.1016/j.soildyn.2022.107349
• Stable GSTC formulation for Maxwell’s equations
  
  • Lebbe N.
  • Pham Kim
  • Maurel Agnès
  IEEE Transactions on Antennas and Propagation, Institute of Electrical and Electronics Engineers, 2022, 70 (8), pp.6825-6840. We revisit the classical zero-thickness Generalized Sheet Transition Conditions (GSTCs) which are a key tool for efficiently designing metafilms able to control the flow of light in a desired way. It is shown that it is more convenient to use an enlarged formulation of the GSTC in which the original metafilm is replaced by GSTCs that exclude the layer from the physical or computational domain. These new "layer" transition conditions have the same form as their "sheet" analogues hence they do not necessitate additional complications in their use; their advantage is that they provide a well-posed problem hence guaranty the stability of numerical schemes in the timedomain. These assessments are demonstrated for an all-dielectric structure; the effective susceptibility tensors are derived thanks to asymptotic analysis combined with homogenization technique and bounds for the susceptibilities entering the balance of energy are provided. While negative constant susceptibilities appear in the classical zero-thickness GSTCs, their values in the enlarged formulation are always positive which ensure the stability of the effective problem. Validation of the effective model is provided by means of comparison with direct numerics in two and three dimensions. (10.1109/TAP.2022.3161436)
  DOI : 10.1109/TAP.2022.3161436
• A numerical package for model order reduction of large dimensional finite element systems of nonlinear vibrating structures based on invariant manifold theory
  
  • Opreni Andrea
  • Vizzaccaro Alessandra
  • Martin Adrien
  • Touzé Cyril
  • Frangi Attilio Alberto
  , 2022. Dimensionality reduction through parametrisation of the system motion along a low dimensional invariant-based span of the phase space represents the most efficient technique for deriving reduced order models (ROM) of structures vibrating with large amplitudes. In this work we present the first release of an efficient software for deriving reduced models of structures based on the Direct Parametrisation of Invariant Manifolds (DPIM). The package exploits an algorithmic implementation of the method tailored for mechanical systems, hence achieving low memory consumption and unprecedented speed. Examples of large scale systems of industrial interest are shown and comparisons with experimental data and full order numerical simulations are reported.
• Comparison of nonlinear methods for reduced-order modeling of geometrically nonlinear structures
  
  • Touzé Cyril
  • Vizzaccaro Alessandra
  • Thomas Olivier
  • Salles Loic
  • Opreni Andrea
  • Shen Yichang
  • Frangi Attilio Alberto
  , 2022. The aim of this contribution is to review and compare three different methods that have been proposed in order to derive reduced-order models for geometrically nonlinear structures, and relying on a nonlinear technique to better take into account the nonlinearities of the initial problem. The three methods are: implicit condensation, quadratic manifold derived with modal derivatives, and projection onto an invariant manifold, tangent at the origin to the linear eigenspace of the master modes. The methods are briefly reviewed theoretically and then compared with dedicated examples.
• Model order reduction for geometrically nonlinear beams featuring internal resonance and centrifugal effect
  
  • Martin Adrien
  • Opreni Andrea
  • Vizzaccaro Alessandra
  • Salles Loic
  • Frangi Attilio Alberto
  • Touzé Cyril
  , 2022. The direct parametrisation of invariant manifold is used for model order reduction of large amplitude vibrations of clampedclamped and rotating cantilever beams. A particular emphasis is set on the computation of the backbone curve in case of internal resonance. For the clamped beam, the 1:5 resonance between first and third mode occuring at large amplitude, is reproduced with the model. For the rotating cantilever, a Campbell diagram is first used to detect the appearance of a 1:5 resonance, which is then computed with the reduction method.
• Asymptotic Computation of Invariant Manifolds of large Finite Element structures with Geometric Nonlinearities
  
  • Vizzaccaro Alessandra
  • Opreni Andrea
  • Salles Loic
  • Frangi Attilio Alberto
  • Touzé Cyril
  , 2022. In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced order dynamics on the manifold. We show the accuracy of the reduction method on selected models, exhibiting large rotations and internal resonances. The results obtained with the reduction compared to full-order harmonic balance simulations show that the proposed methodology can reproduce extremely accurately the dynamics of the original systems with a very low computational cost.