Papers by François Gautier
Journal of Sound and Vibration, Aug 1, 2016
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
HAL (Le Centre pour la Communication Scientifique Directe), 2016
L'effet Trou Noir Acoustique (TN) est une technique passive d'amortissement de vibrations sans aj... more L'effet Trou Noir Acoustique (TN) est une technique passive d'amortissement de vibrations sans ajout de masse fondée sur les propriétés des ondes de flexion dans des structures minces d'épaisseur variable. La mise en oeuvre habituelle consiste en une plaque avec une extrémité profilée selon une loi exponentielle, recouverte d'un film viscoélastique. L'inhomogénéité de la structure conduit à une baisse de la célérité et une augmentation de l'amplitude des ondes de flexion, ce qui a pour conséquence une dissipation d'énergie efficace quand un film amortissant est placé dans la zone de faible épaisseur. Lorsqu'un tel profil est placé à l'extrémité d'une poutre, des caractérisations expérimentales sont possibles à l'aide du coefficient de réflexion ou du recouvrement modal. Des modèles numériques d'une telle structure existent et peuvent aider à comprendre le rôle de la variation d'épaisseur, les effets d'imperfections de fabrication ou encore les effets non-linéaires dus aux faibles épaisseurs.
HAL (Le Centre pour la Communication Scientifique Directe), Apr 11, 2016
L'effet Trou Noir Acoustique (TN) est une technique passive d'amortissement de vibrations sans aj... more L'effet Trou Noir Acoustique (TN) est une technique passive d'amortissement de vibrations sans ajout de masse fondée sur les propriétés des ondes de flexion dans des structures minces d'épaisseur variable. La mise en oeuvre habituelle consiste en une plaque avec une extrémité profilée selon une loi exponentielle, recouverte d'un film viscoélastique. L'inhomogénéité de la structure conduit à une baisse de la célérité et une augmentation de l'amplitude des ondes de flexion, ce qui a pour conséquence une dissipation d'énergie efficace quand un film amortissant est placé dans la zone de faible épaisseur. L'amplitude des ondes à l'extrémité peut facilement atteindre l'ordre de grandeur de l'épaisseur de la plaque, ce qui est une source de non-linéarités géométriques. Ces nonlinéarités peuvent avoir pour conséquences des couplages entre les modes de vibration de la structure, et induire un transfert d'énergie des basses fréquences vers les hautes fréquences. Ce phénomène de transfert d'énergie peut être exploité pour augmenter l'efficacité du traitement dans le domaine des basses fréquences pour lequel le trou noir est peu efficace. Une expérience montre que la terminaison TN se comporte de manière non-linéaire et permet un couplage entre modes. Un régime fortement non-linéaire peut également être observé, qui est associé au phénomène de turbulence d'ondes. Une modélisation d'une poutre TN comme une plaque de von Kármán d'épaisseur variable et une résolution du problème par une méthode modale permet de confirmer les effets observés dans l'expérience et d'analyser plus finement ces résultats.
Journal of Sound and Vibration, May 1, 2009
The aim of this paper is to show that the Image Source Method (ISM) can be used both for analytic... more The aim of this paper is to show that the Image Source Method (ISM) can be used both for analytically calculating Green's functions of particular simply supported convex polygonal plates and for predicting medium and high frequency vibrations of arbitrarily shaped simply supported convex polygonal plates with controllable precision. In the first part of the paper, the method for obtaining the Green's function of a polygonal plate by ISM is developed. Examples for plates of different geometries (rectangle, isosceles right triangle, half-equilateral triangle and equilateral triangle) are given. In the second part of the paper, the pertinence of ISM for predicting medium and high frequency vibrations of arbitrarily shaped simply supported convex polygonal plates is investigated. An approximation based on the exclusion of image sources beyond a certain distance from the receiver is used in order to take advantage of the dissipation of vibrational energy through wave propagation. We investigate the influence of structural damping and truncation distance on the accuracy of such approximation. The computed responses are in good agreement with reference solutions, which are analytically known or obtained by the finite element method.
HAL (Le Centre pour la Communication Scientifique Directe), Jul 3, 2018
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Journal of Sound and Vibration, Jun 1, 2014
Acoustic Black Hole (ABH) effect is a passive vibration reduction technique which takes advantage... more Acoustic Black Hole (ABH) effect is a passive vibration reduction technique which takes advantage of properties of wave propagation in thin structures of varying thickness. A practical implementation of ABH on a uniform beam consists in an extremity whose thickness follows a power-law profile covered by a very thin layer of additional damping material. A modal analysis based on a High Resolution technique shows that the ABH significantly increases the Modal Overlap Factor (MOF) of the beam, thus reducing the resonant behaviour of the structure. Further investigations, including a two dimensional numerical model of the structure based on the finite difference method, show that this MOF can be explained by an increase of the modal density and a high damping of a number of modes of the structure due to the ABH.
International Journal of Solids and Structures, Mar 1, 2022
A unimorph piezoelectric cantilever equipped with an Acoustic Black Hole (ABH) termination is des... more A unimorph piezoelectric cantilever equipped with an Acoustic Black Hole (ABH) termination is designed for broadband energy harvesting. The ABH termination, with its tapered region, induces a focusing of the flexural vibrations which can be used to increase the efficiency of an energy harvesting device. A modal-based analytical model is presented, providing an explicit form of the electro-mechanical coupling for each beam eigenmode. Closed-form expressions for the coupled mechanical response and electrical outputs are obtained, allowing one to draw out a complete parametric study to optimize the device. The optimization procedure is conducted following two steps: first, optimal location and dimensions of a single piezoelectric patch are achieved by maximizing the modal electro-mechanical coupling factor (MEMCF) for each structural mode. Thanks to the proposed analytical approach, it is clearly shown that by putting the piezoelectric patch at the maximum of the strain field in the tapered termination, and by adjusting its length in accordance with the focalization created by the ABH effect, the ABH cantilever produces much higher MEMCFs over a wide frequency range and thus outperforms those of a uniform beam. Second, optimization of the shunted circuit is comprehensively performed for a circuit with only resistance, or both resistance and inductance, in series or in parallel. Analytical results show that the key design rule resides in matching the time scale of the circuit with that of the forcing frequency. Addition of the inductance allows enhancing the performance, but on a narrow frequency band. Finally, broadband advantages can be further obtained by considering multiple piezoelectric patches, in which the optimum is obtained when the shunted circuit in each patch is tuned targeting an eigenmode of the ABH beam.
HAL (Le Centre pour la Communication Scientifique Directe), Apr 23, 2012
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Mechanical Systems and Signal Processing, Nov 1, 2013
The mechanical characteristics of wood panels used by instrument makers are related to numerous f... more The mechanical characteristics of wood panels used by instrument makers are related to numerous factors, including the nature of the wood or characteristic of the wood sample (direction of fibers, micro-structure nature). This leads to variations in the Young's modulus, the mass density, and the damping coefficients. Existing methods for estimating these parameters are not suitable for instrument makers, mainly because of the need of expensive experimental setups, or complicated protocols, which are not adapted to a daily practice in a workshop. In this paper, a method for estimating the Young's modulus, the mass density, and the modal loss factors of flat panels, requiring a few measurement points and an affordable experimental setup, is presented. It is based on the estimation of two characteristic quantities: the modal density and the mean mobility. The modal density is computed from the values of the modal frequencies estimated by the subspace method
International Journal of Non-linear Mechanics, Sep 1, 2017
Acoustic Black Hole eect (ABH) is a passive vibration damping technique without added mass based ... more Acoustic Black Hole eect (ABH) is a passive vibration damping technique without added mass based on exural waves properties in thin structures with variable thickness. A common implementation is a plate edge where the thickness is locally reduced with a power law prole and covered with a viscoelastic layer. The plate displacement in the small thickness region is large and easily exceeds the plate thickness. This is the origin of geometric nonlinearity which can generate couplings between linear eigenmodes of the structure and induce energy transfer between low and high frequency regimes. This phenomenon may be used to increase the eciency of the ABH treatment in the low frequency regime where it is usually inecient. An experimental investigation evidenced that usual ABH implementation gives rise to measurable geometric nonlinearity and typical nonlinear phenomena. In particular, strongly nonlinear regime and wave turbulence are reported. The nonlinear ABH beam is then modeled as a von Kármán plate with variable thickness. The model is solved numerically by using a modal method combined with an energy-conserving time integration scheme. The eects of both the thickness prole and the damping layer are then investigated in order to improve the damping properties of an ABH beam. It is found that a compromise between the two eects can lead to an important gain of eciency in the low frequency range.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 17, 2019
Acoustic Black Hole effect (ABH) describes a passive vibration mitigation technique used to damp ... more Acoustic Black Hole effect (ABH) describes a passive vibration mitigation technique used to damp out the flexural vibrations of thin structures such as beams. It relies on a wedge profile where the thickness is gradually decreasing, so that wave velocities slows down, potentially decaying to zero without reflection. The device generally shows very interesting damping properties in the mid and high-frequency range, however its efficiency in the low-frequency range still remains limited. In this contribution, the inclusion of a nonlinearity as a way to improve the low-frequency performance of an ABH is investigated. Indeed, the nonlinearity may be used as a vector to transfer energy from the low to the high frequency range, where the damping properties are much more significant. Two different mechanisms are tested, based respectively on geometric and contact nonlinearity.
Journal of Sound and Vibration, Feb 1, 2016
The so-called "acoustic black hole" effect (ABH) is a passive vibration control technique based o... more The so-called "acoustic black hole" effect (ABH) is a passive vibration control technique based on the flexural waves properties in thin structure of varying thickness. A usual implementation consists in using a plate with tapered extremity with a power-law profile, covered with a thin damping layer. The inhomogeneity of the structure leads to a decrease of flexural wave speed and an increase of their amplitude, therefore resulting in an efficient energy dissipation if damping layer is placed where the thickness is minimal. The manufacture of an efficient extremity is difficult because of the small thickness, and often generates imperfections and tearing. Moreover, previous works suggest multiple that flexural modes are propagating across the width of the ABH tip. A model of an ABH multimodal waveguide taking into account an imperfect termination is developed. It shows that an elementary imperfection can affect the reflection coefficient of the extremity and reduce it. Scattering and propagation properties of the extremity
Journal of Sound and Vibration, Aug 1, 2015
The flexural waves propagating in a beam can be efficiently absorbed if one extremity is tapered ... more The flexural waves propagating in a beam can be efficiently absorbed if one extremity is tapered with a power law profile and covered by a thin layer of additional damping material. Such a termination induces the so-called "acoustic black hole effect" (ABH): if the thickness decreases locally, flexural waves slow down and the amplitude of the displacement field increases, leading to efficient energy dissipation if an absorbing layer is placed where the thickness is minimum. This paper presents a specific study of the reflection coefficient of ABH beam terminations. A Kundt-like measurement method of the reflection coefficient of a beam termination is proposed. The method is validated using theoretical results in the case of a beam free end. Results for several ABH extremities show a clear decrease of the modulus of the reflection coefficient R. The phase of R due to the decreasing thickness profile is also investigated and is interpreted by defining a correction length for the tapered termination. These experimental results are compared with several models: geometrical acoustics based model, beam waveguide model
HAL (Le Centre pour la Communication Scientifique Directe), Apr 12, 2010
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 1, 2011
The differences of assessment between musical instruments of the same kind (e.g classical guitars... more The differences of assessment between musical instruments of the same kind (e.g classical guitars) covers aspects linked to sounds, expressibility, or even manufacturing process. How to extract relevant information related to these aspects by measuring well chosen physical (acoustical, vibratory) parameters ? The aim of the proposed study is to identify criteria enabling the clustering of string instruments in different classes. The plucked instruments will be our application. The knowledge of these parameters would then allow to give an help to the instrument maker in the adjustments and settings likely to be made on an instrument. The modal parameters (frequency, and damping coefficient) can be estimated accurately on a large frequency range from impulse responses by using the high-resolution ESPRIT method, associated with the ESTER criterion to enumerate the signal components. Global parameters, such as the modal density, loss factors and modal overlap factor can be determined and used to estimate average mobility, derived from Skudrzyk's mean-value theorem. The application on guitars and ukulele shows a common behavior of their average mobility: it remains constant in the mid and high frequency domains. The corresponding value is used as one of the parameters enabling the characterization.
HAL (Le Centre pour la Communication Scientifique Directe), Apr 23, 2012
HAL (Le Centre pour la Communication Scientifique Directe), Aug 29, 2011
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
HAL (Le Centre pour la Communication Scientifique Directe), Aug 29, 2011
Le grincement est un bruit induit par le frottement dont la nature fugace est très souvent mise e... more Le grincement est un bruit induit par le frottement dont la nature fugace est très souvent mise en avant expérimentalement. Cet article présente l'étude menée sur un modèle de principe, contenant deux masses en contact frottant et obtenu suite à l'évolution du modèle classique de stick-slip par une démarche de complexité croissante. Alors que l'étude temporelle menée sur ce modèle permet de mettre en évidence l'extrême sensibilité du grincement vis-à-vis des paramètres de contrôle, l'étude modale permet de comprendre l'origine de cette sensibilité grâce au concept d'instabilité par couplage modal.
Sandwich honeycomb panels are widely used in aerospace applications because they are very light a... more Sandwich honeycomb panels are widely used in aerospace applications because they are very light and stiff. Strong mechanical or acoustical excitations, associated to low damping properties of such panels can lead to high vibration levels, generating fatigue and reliability problems. We propose in this paper to investigate the capability of micro-perforations of honeycomb panels for reducing their vibration levels. Micro-perforations are mostly known and used in acoustics for increasing absorption. A model of the panel vibration damping induced by the acoustic motion in the micro-perforations is proposed here. For this purpose, a lumped element model, based on Maa's results is developped for estimating a viscous damping force at the micro-scale. The resultant force is then homogenized for a group of cells (meso-scale model) and allows us to express a damping term for the global structure (macro-scale model). A perturbation technique is then used to compute the modal damping coefficients of a micro-perforated plate in order to evaluate the performance of the treatment.
HAL (Le Centre pour la Communication Scientifique Directe), Dec 7, 2020
The design of lightweight and stiff structures with attractive vibration damping properties is a ... more The design of lightweight and stiff structures with attractive vibration damping properties is a major issue in mechanical engineering. The insertion of Acoustic Black Holes (ABH) is an innovative technique that consists in locally reducing the thickness of the stucture and coating it with a viscoelastic film. In the particular case where the damping layer provides a perfect adjustment of the losses, the reflection coefficient R of the resulting system is zero at the resonance of a trapped mode localized in the ABH profile. This phenonemon is reached when the critical coupling conditions are fulfilled. However, the precise amount of losses is particularly difficult to tune by using only classical viscoelastic layers. It is here proposed to control it by using a thermal active system acting in a shape memory polymer (SMP). The goal of the paper is to investigate several enhanced ABH (eABH) in beams for which the damping and the stiffness are controlled by a thermal profile. For each eABH configuration, the trajectory of the zeros of R is studied in order to approach the critical coupling conditions.
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Papers by François Gautier