Papers by Jean-Mathieu Mencik
Journal of Computational and Applied Mathematics, 2024
Model reduction based on matrix interpolation provides an efficient way to compute the dynamic re... more Model reduction based on matrix interpolation provides an efficient way to compute the dynamic response of nearly periodic structures composed of substructures (cells) with varying properties. This may concern 2D or 3D substructures subjected to geometric modifications (mesh variations) or more classic dimension changes. An efficient interpolation strategy for a nearly periodic structure can be obtained by (i) interpolating reduced substructure matrices over a multi-dimensional parametric space and (ii) reducing the number of degrees of freedom at substructure boundaries by considering the interface modes of an equivalent purely periodic structure. In this paper, two basis enrichment techniques are proposed to improve the accuracy of the interpolation strategy. This consists in (i) considering high-order static modes, in addition to component modes, to express the reduced substructure matrices and (ii) adding static correction vectors into the basis of interface modes to account for the varying properties of the substructures. Numerical experiments are carried out which clearly highlight the relevance of the basis enrichment techniques for predicting the harmonic behavior of nearly periodic structures with 2D or 3D substructures.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 24, 2015
European Journal of Mechanics A-solids, 2023
HAL (Le Centre pour la Communication Scientifique Directe), Sep 12, 2022
A finite element-based approach is proposed to compute the time response of infinite periodic str... more A finite element-based approach is proposed to compute the time response of infinite periodic structures with local nonlinearities. Under the assumption that the excitation sources and the nonlinear effects are localized, an infinite periodic structure can be modeled as a finite one with two left and right semi-infinite linear parts which are described via appropriate absorbing boundary conditions (BCs) formulated in the time domain using the wave finite element (WFE) method as recently proposed by the authors in [1]. The formulation of the absorbing BCs involves the usual vectors of displacements, velocities and accelerations, as well as vectors of supplementary variables. In this way, a classical second-order time differential equation for a nonlinear finite periodic structure with absorbing BCs can be formulated and integrated into a Newmark's algorithm for the temporal variable and a Newton Raphson's algorithm for the nonlinear equations. Numerical experiments are proposed which highlight the relevance of the approach for several types and levels of nonlinearities.
HAL (Le Centre pour la Communication Scientifique Directe), Sep 12, 2022
The acoustic radiation of 2D nearly periodic plates interacting with light fluids is addressed. M... more The acoustic radiation of 2D nearly periodic plates interacting with light fluids is addressed. Metamaterial plates made up of resonant multi-layered cells/substructures with varying (random) geometrical properties, which are described via distorted finite element meshes, are dealt with. The proposed approach involves the Craig-Bampton method and an interpolation scheme for modeling the substructures and approximating the related reduced mass and stiffness matrices. In this paper, this approach is applied to compute the radiation efficiencies of such metamaterial plates with the method of elementary radiators. The relevance of the proposed approach is highlighted through numerical experiments. Especially the structural and acoustic responses of a nearly periodic plate are assessed and compared to the purely periodic case.
HAL (Le Centre pour la Communication Scientifique Directe), 2019
HAL (Le Centre pour la Communication Scientifique Directe), May 16, 2022
Méthode adaptative de réduction de modèles par sous-structuration en présence de variabilité géom... more Méthode adaptative de réduction de modèles par sous-structuration en présence de variabilité géométrique et d'incertitudes paramétriques
Mechanical Systems and Signal Processing, May 1, 2023
HAL (Le Centre pour la Communication Scientifique Directe), Jul 5, 2016
This paper addresses the issue of quantifying uncertainty bounds when updating the finite element... more This paper addresses the issue of quantifying uncertainty bounds when updating the finite element model of a mechanical structure from measurement data. The problem arises as to assess the validity of the parameters identification and the accuracy of the results obtained. In this paper, a covariance estimation procedure is proposed about the updated parameters of a finite element model, which propagates the data-related covariance to the parameters by considering a first-order sensitivity analysis. In particular, this propagation is performed through each iteration step of the updating minimization problem, by taking into account the covariance between the updated parameters and the data-related quantities. Numerical simulations on a beam show the feasibility and the effectiveness of the method.
HAL (Le Centre pour la Communication Scientifique Directe), Sep 1, 2021
This paper addresses the issue of quantifying uncertainty bounds when updating the finite element... more This paper addresses the issue of quantifying uncertainty bounds when updating the finite element model of a mechanical structure from measurement data. The problem arises as to assess the validity of the parameters identification and the accuracy of the results obtained. In this paper, a covariance estimation procedure is proposed about the updated parameters of a finite element model, which propagates the data-related covariance to the parameters by considering a first-order sensitivity analysis. In particular, this propagation is performed through each iteration step of the updating minimization problem, by taking into account the covariance between the updated parameters and the data-related quantities. Numerical simulations on a beam show the feasibility and the effectiveness of the method.
European Journal of Mechanics A-solids, 2022
International audienc
Le Centre pour la Communication Scientifique Directe - HAL - Université Francois Rabelais - Tours, Sep 12, 2022
A wave finite element (WFE) strategy to predict and localize defects in networks of straight pipe... more A wave finite element (WFE) strategy to predict and localize defects in networks of straight pipes with curved joints is proposed. This involves estimating the times of flight taken by some narrow wave packets to get transmitted through or reflected by a coupling element that could represent either a joint or a defect. The ansatz proposed here is to define these times of flight from the frequency derivatives of the arguments of the scattering matrix of the coupling element. Also, the times of flight taken by wave packets to travel along a certain pipe can be classically obtained from the analysis of the group velocities. By comparing the theoretical expressions of the times of flight with those recorded in a network of pipes at some measurement point, it becomes possible to localize a defect with accurate precision and, also, to have a physical insight about the kind of waves which are transmitted through a joint and reflected by a defect (pathways). Numerical experiments are carried out which highlight the relevance and applicability of the proposed approach.
Proceedings of the XXXVIII Iberian Latin American Congress on Computational Methods in Engineering, 2017
28th ISMA conference on Noise and Vibration Engineering, Sep 17, 2018
International audienc
28th ISMA conference on Noise and Vibration Engineering, Sep 17, 2018
International audienceA wave finite element (WFE) based approach is proposed to analyze the dynam... more International audienceA wave finite element (WFE) based approach is proposed to analyze the dynamic behavior of finite-length periodic structures which are made up of identical substructures but also contain several substructures whose material and geometric characteristics are slightly perturbed. Within the WFE framework, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two unperturbed substructures, and considering perturbed parts which are composed of perturbed substructures surrounded by two unperturbed ones. In doing so, a few wave modes are only required for modeling the central periodic structure, outside the perturbed parts. For forced response computation purpose, a reduced wave-based matrix formulation is established which follows from the consideration of transfer matrices between the right and left sides of the perturbed parts. Numerical experiments are carried out on a periodic 2D str...
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Papers by Jean-Mathieu Mencik