Jean LERBET | Evry University (original) (raw)
Papers by Jean LERBET
Communications in Algebra, Mar 11, 2021
Abstract The main topic of this paper is to compute the first relative cohomology group of the Li... more Abstract The main topic of this paper is to compute the first relative cohomology group of the Lie algebra of smooth vector fields with coefficients in the space of trilinear differential operators that acts on tensor densities, vanishing on the Lie algebra where and
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HAL (Le Centre pour la Communication Scientifique Directe), Mar 24, 2021
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Journal of Applied Mathematics and Mechanics, Jun 4, 2023
This paper provides an explicit geometric and coordinate‐free formulation of incremental discrete... more This paper provides an explicit geometric and coordinate‐free formulation of incremental discrete mechanics in the framework of potentially non integrable hypoelasticity. First, the general framework is developed in order to tackle hypoelasticity as an Ehresmann connection on the cotangent bundle . Two types of incremental evolutions may be distinguished, the weak or integrable incremental evolutions and the strong or non integrable incremental evolutions, according to the nature of the hypoelastic constitutive law. The geometric structure of the double tangent bundle is fully used in order to get the geometric counterpart κ of the so‐called tangent stiffness matrix. Subject to specific conditions in , the incremental evolution is then a well‐founded question. An hypoelastic four‐grains granular system illustrates in detail these general results.
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HAL (Le Centre pour la Communication Scientifique Directe), Oct 30, 2009
International audienc
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Elsevier eBooks, 2018
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HAL (Le Centre pour la Communication Scientifique Directe), Nov 20, 2020
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Meccanica
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This paper proposes a new detection technique applied on electroencephalogram (EEG) signals which... more This paper proposes a new detection technique applied on electroencephalogram (EEG) signals which were measured on Parkinsonian rats during an experiment. Our technique uses a recursive filter-bank-based implementation of the short-time Fourier transform that is sharpened using several time-frequency reassignment methods. A detector is then applied to the obtained representation to allow an identification of the HVS signals which are specific to subjects with neurodegeneratives diseases. Our results show an improvement of the state of the art while paving the way of a real-time implementation.
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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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Multibody System Dynamics
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HAL (Le Centre pour la Communication Scientifique Directe), Dec 20, 2013
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HAL (Le Centre pour la Communication Scientifique Directe), Aug 21, 2016
International audienc
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HAL (Le Centre pour la Communication Scientifique Directe), Aug 23, 2021
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Multi-Body Kinematics and Dynamics with Lie Groups, 2018
In the previous chapters all the necessary formula for expanding kinematics or dynamics of any tr... more In the previous chapters all the necessary formula for expanding kinematics or dynamics of any tree structured rigid body system were exposed. In the present chapter we consider a rigid body system which is a chain of bodies linking up two bodies a and b . Then, with the notation.
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We are interested in buckling for Timoshenko beam supported along its length by an elastic wall (... more We are interested in buckling for Timoshenko beam supported along its length by an elastic wall (Winkler foundation) and subjected to a longitudinal force. We use analytical methods to determine buckling load and mode shape rather than numerical methods. Haringx and Engesser models are compared. We show that the rigidity of the wall solely gouverns the phenomena and that the two models are equivalent whatever the parameters of the problem.
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HAL (Le Centre pour la Communication Scientifique Directe), Aug 22, 2021
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Journal of Engineering Mechanics-asce, Sep 1, 2022
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International audienc
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International audienceThe present study theoretically investigates the free vibration problem of ... more International audienceThe present study theoretically investigates the free vibration problem of a discrete granular system. This micro structured system consists of uniform grains elastically connected by shear and rotation springs. Such a granular structural system is confined by discrete elastic interactions, to take into account the lateral granular contributions. This discrete repetitive system could be considered as a discrete Cosserat chain or a lattice elastic model with shear interaction. First, from the vibration equation governing the model, the natural frequencies are exactly calculated for the simply supports boundary conditions. Then it is shown that the discrete equations of this granular system, for an infinite number of grains, converge to the differential equations of the Bresse-Timoshenko beam resting on Winkler foundation. A gradient Bresse-Timoshenko model is constructed from continualization of the difference equations of the granular system. The natural freque...
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Communications in Algebra, Mar 11, 2021
Abstract The main topic of this paper is to compute the first relative cohomology group of the Li... more Abstract The main topic of this paper is to compute the first relative cohomology group of the Lie algebra of smooth vector fields with coefficients in the space of trilinear differential operators that acts on tensor densities, vanishing on the Lie algebra where and
Bookmarks Related papers MentionsView impact
HAL (Le Centre pour la Communication Scientifique Directe), Mar 24, 2021
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Journal of Applied Mathematics and Mechanics, Jun 4, 2023
This paper provides an explicit geometric and coordinate‐free formulation of incremental discrete... more This paper provides an explicit geometric and coordinate‐free formulation of incremental discrete mechanics in the framework of potentially non integrable hypoelasticity. First, the general framework is developed in order to tackle hypoelasticity as an Ehresmann connection on the cotangent bundle . Two types of incremental evolutions may be distinguished, the weak or integrable incremental evolutions and the strong or non integrable incremental evolutions, according to the nature of the hypoelastic constitutive law. The geometric structure of the double tangent bundle is fully used in order to get the geometric counterpart κ of the so‐called tangent stiffness matrix. Subject to specific conditions in , the incremental evolution is then a well‐founded question. An hypoelastic four‐grains granular system illustrates in detail these general results.
Bookmarks Related papers MentionsView impact
HAL (Le Centre pour la Communication Scientifique Directe), Oct 30, 2009
International audienc
Bookmarks Related papers MentionsView impact
Elsevier eBooks, 2018
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HAL (Le Centre pour la Communication Scientifique Directe), Nov 20, 2020
Bookmarks Related papers MentionsView impact
Meccanica
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This paper proposes a new detection technique applied on electroencephalogram (EEG) signals which... more This paper proposes a new detection technique applied on electroencephalogram (EEG) signals which were measured on Parkinsonian rats during an experiment. Our technique uses a recursive filter-bank-based implementation of the short-time Fourier transform that is sharpened using several time-frequency reassignment methods. A detector is then applied to the obtained representation to allow an identification of the HVS signals which are specific to subjects with neurodegeneratives diseases. Our results show an improvement of the state of the art while paving the way of a real-time implementation.
Bookmarks Related papers MentionsView impact
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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Multibody System Dynamics
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HAL (Le Centre pour la Communication Scientifique Directe), Dec 20, 2013
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HAL (Le Centre pour la Communication Scientifique Directe), Aug 21, 2016
International audienc
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HAL (Le Centre pour la Communication Scientifique Directe), Aug 23, 2021
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Multi-Body Kinematics and Dynamics with Lie Groups, 2018
In the previous chapters all the necessary formula for expanding kinematics or dynamics of any tr... more In the previous chapters all the necessary formula for expanding kinematics or dynamics of any tree structured rigid body system were exposed. In the present chapter we consider a rigid body system which is a chain of bodies linking up two bodies a and b . Then, with the notation.
Bookmarks Related papers MentionsView impact
We are interested in buckling for Timoshenko beam supported along its length by an elastic wall (... more We are interested in buckling for Timoshenko beam supported along its length by an elastic wall (Winkler foundation) and subjected to a longitudinal force. We use analytical methods to determine buckling load and mode shape rather than numerical methods. Haringx and Engesser models are compared. We show that the rigidity of the wall solely gouverns the phenomena and that the two models are equivalent whatever the parameters of the problem.
Bookmarks Related papers MentionsView impact
HAL (Le Centre pour la Communication Scientifique Directe), Aug 22, 2021
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Journal of Engineering Mechanics-asce, Sep 1, 2022
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International audienc
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International audienceThe present study theoretically investigates the free vibration problem of ... more International audienceThe present study theoretically investigates the free vibration problem of a discrete granular system. This micro structured system consists of uniform grains elastically connected by shear and rotation springs. Such a granular structural system is confined by discrete elastic interactions, to take into account the lateral granular contributions. This discrete repetitive system could be considered as a discrete Cosserat chain or a lattice elastic model with shear interaction. First, from the vibration equation governing the model, the natural frequencies are exactly calculated for the simply supports boundary conditions. Then it is shown that the discrete equations of this granular system, for an infinite number of grains, converge to the differential equations of the Bresse-Timoshenko beam resting on Winkler foundation. A gradient Bresse-Timoshenko model is constructed from continualization of the difference equations of the granular system. The natural freque...
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