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International audience; This paper addresses the problem of estimating the local viscoelastic parameters of sandwich beams. An original procedure involving an inverse vibratory method (Force Analysis Technique) and the Timoshenko beam theory is detailed and applied experimentally on a sample presenting a honeycomb core. The major philosophy relies in considering multi-layer beams as equivalent homogeneous structures. This simplified approach is thought to be more representative of the global dynamic behaviour, in addition the reduction of degrees of freedom is obviously an improvement for modelling on Finite Element software.When compared to other usual approaches, the method developed in this paper shows a very good agreement between the experimental sandwich beam and the homogeneous model, which highlights interesting insights for applying it to industrial structures. The local aspect, the robustness and the self-regularization properties are verified on a wide frequency range, making the procedure possibly efficient for characterization of structures on a production line, flaw detection and Structural Health Monitoring.

Time Reversal (TR) concept has been proposed in the 1980s by Mathias Fink and colleagues, it is based on the symmetry of vibrations governing equations for positive and negative time, when damping effect is negligible. The main consequence of this property is the possibility of creating time reversed waves travelling back to the location where the primary waves were created. Several applications in bio mechanics, military purposes, room acoustics, structural vibrations and ultrasonics for SHM applications have been developed in literature. We just give here few papers for illustrating the different treated aspects [1, 2, 3, 4, 5, 6]

International audience; A damage identification method named virtual vibration deflection (VVD) was developed, the principle of which was formulated based on the “weak” modality of the pseudo-excitation (PE) approach previously established. In essence, VVD is based on locating structural damage within a series of “sub-regions” divided from the entire structure under inspection, and each sub-region was considered as a “virtual” structure undergoing independent vibration. The corresponding vibration deflection of the “virtual” structure was then used to derive the damage index of VVD. Besides various advantages inheriting from the PE approach, for example, capability of detecting damage without baseline signals and pre-developed benchmark structures, VVD exhibits improved detection accuracy and particularly enhanced noise immunity compared with the PE approach, attributed to a hybrid use of multi-types of vibration signatures (MTVS). As a proof-of-concept investigation, a beam model was used in a numerical study to examine the philosophy of VVD. And the influences from different factors (i.e., level of measurement noise and measurement density) on the detection accuracy of VVD were discussed based on the numerical model. An experiment was carried out subsequently to identify the locations of multiple defects contained in an aluminum beam-like structure. Identification results constructed by the PE approach, VVD using single-type of vibration signatures, and VVD using MTVS, were presented, respectively, for the purpose of comparison.

International audience; The source field reconstruction aims at identifying the excitation field measuring the response of the system. In Near-field Acoustic Holography, the response of the system (the radiated acoustic pressure) is measured on a hologram using a microphones array and the source field (the acoustic velocity field) is reconstructed with a back-propagation technique performed in the wave number domain. The objective of the present works is to use such a technique to reconstruct displacement field on the whole surface of a plate by measuring vibrations on a one-dimensional holograms. This task is much more difficult in the vibratory domain because of the complexity of the equation of motion of the structure.The method presented here and called "Structural Holography" is particularly interesting when a direct measurement of the velocity field is not possible. Moreover, Structural Holography decreases the number of measurements required to reconstruct the displacement field of the entire plate. This method permits to separate the sources in the case of multi-sources excitations by considering them as direct or back waves. It's possible to compute the structural intensity of one particular source without the contributions of others sources.The purpose of this paper is to introduce the Structural Holography method. The first part presents the theoretical background of the method. A numerical simulation of displacement fields generate by few sources for an infinite plate is presented in a second part. The structural intensity for each source is computed by removing the contribution of others source. Finally, some results are presented for a simply supported plate.

International audience; This article presents the modeling of a MEMS microphone with an original architecture formed of mechanical structures moving in the plane of the substrate. On the contrary of most microphones generally constituted of an oscillating membrane, some transducers developed by the CEA-LETI with M&NEMS technology use micro beams moving in the plane of the silicon wafer under the effect of an acoustical wave. These micro-structures are connected to the substrate by flexible micro-hinge and strain silicon nano-gauge producing a variation in resistance by piezoresistive effect. After the description of the design and functioning of the microphone under study, the vibroacoustic model of the fluid-structure coupling is presented. Considering the dimensions of the MEMS transducer close to the thermal and viscous boundary layers thicknesses, this model has to include diffusion phenomena. The model is discretized using the finite element method and the weak formulation is implemented using COMSOL Multiphysics® software. The pressure sensitivity of the microphone is calculated and compared with an analytical lumped model to asses the numerical model. Pressure and velocity fileds are also computed. Solutions of simulations are interpreted by focusing on phenomena influencing the sensitivity of this novel sensor design. In particular, the influence of the geometry and the role of the different part of the transducer (back cavity, mechanical structures) are studied.

International audience; An as diffuse as possible acoustic field is pursued when performing measurements that make use of a reverberant room. The diffusivity descriptors that are commonly used to qualify the actual sound field in such a room are calculated in the room volume, away from boundaries. This is somewhat contradictory with the fact that for sound insulation and sound absorption measurements as examples, specimens are placed at room boundaries either a wall or the floor. This work presents a characterization of the sound pressure field at the boundaries of a reverberant room in order to evaluate the diffusivity of the excitation at these specific locations. A boundary diffuse field index is proposed, numerically evaluated and then tested in two reverberant chambers in steady state conditions. It is shown that this index allows evaluating the boundary diffusivity in a given reverberant room according to its geometry and other relevant parameters, such as the sound source location or the presence of sound diffusers.

International audience; The City Lightweight and Innovative Cab (CLIC) project was a scientific collaboration gathering public and private organizations. The aim was to propose an innovative lighten truck cab, where a high strength steel was used. As long as it could affect directly the acoustic environment of the cab, it was necessary to be able to simulate the vibroacoustic behavior of the truck cab in the mid frequency range. The dissipative treatments used for noise and vibration control such as viscoelastic patches and acoustic absorbing materials must then be taken into account in the problem. A process based on the SmEdA (Statistical modal Energy distribution Analysis) method was developed and is presented in this paper. SmEdA allows us substructuring the global problem, to study the interaction between the floor and the interior cavity. The process consists in building finite element models (FEM) of each subsystem (floor, internal cavity), including the dissipative material (damping layer, poroelastic material). Standard modal FEM calculations are then performed for each uncoupled subsystem. From the spatial mode shapes, and the modal strain -kinetic energies, the modal loss factors of both subsystems are estimated. Finally, the pressure levels inside the cavity are deduced from the resolution of the SmEdA equations. To validate this process, a truck cabin has been excited mechanically on a rail of the floor and the pressure levels at different positions inside the cabin were measured for different configurations of dissipative treatment. Comparisons between SmEdA and experimental results allows us to assess the accuracy of the proposed method.

International audience; The irrotational part of the structural intensity for flexural wave motion in plate-like structures is calculated from measurement data of kinematic quantities, such as out-of-plane velocities, by a new method that makes use of a test functional series expansion. The computation of the structural intensity and its irrotational part, which allows to effectively assess vibrational sources and sinks, is less sensitive to measurement noise as compared to standard approaches.

International audience; Nowadays, the need of source identification methods is still growing and application cases are more and more complex. As a consequence, it is necessary to develop methods allowing us to reconstruct sound fields on irregularly shaped sources in reverberant or confined acoustic environment. The inverse Patch Transfer Functions (iPTF) method is suitable to achieve these objectives. Indeed, as the iPTF method is based on Green's identity and double measurements of pressure and particle velocity on a surface surrounding the source, it is independent of the acoustic environment. In addition, the finite element solver used to compute the patch transfer functions permits us to handle sources with 3D irregular shapes. In the present paper, two experimental applications on a flat plate and an oil pan have been carried out to show the performances of the method on real applications. As for all ill-posed problem, it is shown that the crucial point of this method is the choice of the parameter of the Tikhonov regularization, one of the most widely used in the literature. The classical L-curve strategy sometimes fails to choose the best solution. This issue is clearly explained and an adapted strategy combining L-curve and acoustic power conservation is proposed. The efficiency of this strategy is demonstrated on both applications and compared to results obtained with Generalized Cross Validation (GCV) technique.

International audience; A damage characterization framework based on the “pseudo-excitation” (PE) approach has recently been established, aimed at quantitatively identifying damage in beam-, plate-, and shell-like structural components. However, it is envisaged that the effectiveness of the PE approach can be restricted in practical implementation, due to the involvement of high-order derivatives of structural dynamic deflections, in which measurement noise and uncertainties can overwhelm the damage-associated signal features upon mathematical differentiation. In this study, the PE approach was revamped by introducing the weighted integration, whereby the prerequisite of satisfying the local equilibrium conditions was relaxed from “point-by-point” to “region-by-region”. The revamped modality was thus colloquially referred to as “weak formulation” of the PE approach, as opposed to its original version which is contrastively termed as “strong formulation”. By properly configuring a weight function, noise immunity of the PE approach was enhanced, giving rise to improved detection accuracy and precision even under noisy measurement conditions. Furthermore, the ‘weak formulation’ was extended to a series of coherent variants through partial integration, rendering a multitude of detection strategies by selecting measurement parameters and configurations. This endowed the PE approach with flexibility in experimental manipulability, so as to accommodate various detection requirements. As an application of the “weak formulation”, a continuous gauss smoothing (CGS)-based detection scheme was developed, and validated by localizing multiple cracks in a beam structure, showing fairly improved noise tolerance.

Research highlights: -Vibroacoustics modeling of dissipative treatments in the mid-frequency domain. -Equivalent models for viscoelastic and poroelastic materials. -Galerkin procedure with normal modes for estimating the modal damping loss factors. -Application to plate-cavity test cases with different dissipative treatments. -Comparisons of predicted and measured subsystem energy ratios up to 8 kHz; International audience; Vibro-acoustic simulation in the mid-frequency range is of interest for automotive and truck constructors. The dissipative treatments used for noise and vibration control such as viscoelastic patches and acoustic absorbing materials must be taken into account in the problem. The Statistical modal Energy distribution Analysis (SmEdA) model consists in extending Statistical Energy Analysis (SEA) to the mid-frequency range by establishing power balance equations between the modes of the different subsystems. The modal basis of uncoupled-subsystems that can be estimated by the finite element method in the mid-frequency range is used as input data. SmEdA was originally developed by considering constant modal damping factors for each subsystem. However, this means that it cannot describe the local distribution of dissipative materials. To overcome this issue, a methodology is proposed here to take into account the effect of these materials. This methodology is based on the finite element models of the subsystems that include well-known homogenized material models of dissipative treatments. The Galerkin method with subsystem normal modes is used to estimate the modal damping loss factors. Cross-modal coupling terms which appear in the formulation due to the dissipative materials are assumed to be negligible. An approximation of the energy sharing between the subsystems damped by dissipative materials is then described by SmEdA. The different steps of the method are validated experimentally by applying it to a laboratory test case composed of a plate-cavity system with different configurations of dissipative treatments. The comparison between the experimental and the simulation results shows good agreement in the mid-frequency range.

International audience; This paper presents a method of determining an appropriate equation of motion of two-dimensional plane structures like membranes and plates from vibration response measurements. The local steady-state vibration field is used as input for the inverse problem that approximately determines the dispersion curve of the structure. This dispersion curve is then statistically treated with Akaike information criterion (AIC), which compares the experimentally measured curve to several candidate models (equations of motion). The model with the lowest AIC value is then chosen, and the utility of other models can also be assessed. This method is applied to three experimental case studies: A red cedar wood plate for musical instruments, a thick paper subjected to unknown membrane tension, and a thick composite sandwich panel. These three cases give three different situations of a model selection.

International audience; While the structural-acoustic coupling between flexible structures and closed acoustic cavities has been extensively studied in the literature, the modeling of structures coupled through open cavities, especially connected in cascade, is still a challenging task for most of the existing methods. The possible presence of micro-perforated panels (MPPs) in such systems adds additional difficulties in terms of both modeling and physical understanding. In this study, a sub-structuring methodology based on the Patch Transfer Function (PTF) approach with a Compound Interface treatment technique, referred to as CI-PTF method, is proposed, for dealing with complex systems involving cascade open/closed acoustic cavities and MPPs. The co-existence of apertures and solid/flexible/micro-perforated panels over a mixed separation interface is characterized using a compound panel subsystem, which enhances the systematic coupling feature of the PTF framework. Using several typical configurations, the versatility and efficiency of the proposed method is illustrated. Numerical studies highlight the physical understanding on the behavior of MPP inside a complex vibroacoustic environment, thus providing guidance for the practical design of such systems.

International audience; A method fo rreconstructing and separating vibratory field on a plate-like structure is presented. The method, called “Structural Holography” is derived from classical Near-field Acoustic Holography (NAH) but in the vibratory domain. In this case, the plate displacement is measured on one-dimensional lines (the holograms) and used to reconstruct the entire two-dimensional displacement field. As a consequence, remote measurements on non directly accessible zones are possible with Structural Holography. Moreover, as it is based on the decomposition of the field into forth and back waves, Structural Holography permits to separate forces in the case of multi-sources excitation. The theoretical back-ground of the Structural Holography method is described first. Then, to illustrate the process and the possibilities of Structural Holography, the academic test case of an infinite plate excited by few point forces is presented. With the principle of vibratory field separation, the displacement fields produced by each point force separately is reconstructed. However, the displacement field is not always meaningful and some additional treatments are mandatory to localize the position of point forces for example. From the simple example of an infinite plate, a post-processing based on the reconstruction of the structural intensity field is thus proposed. Finally, Structural Holography is generalized to finite plates and applied to real experimental measurements.

International audience; This paper presents the theoretical framework of the virtual acoustic volume concept and two related inverse Patch Transfer Functions (iPTF) identification methods (called u-iPTF and m-iPTF depending on the chosen boundary conditions for the virtual volume). They are based on the application of Green's identity on an arbitrary closed virtual volume defined around the source. The reconstruction of sound source fields combines discrete acoustic measurements performed at accessible positions around the source with the modal behavior of the chosen virtual acoustic volume. The mode shapes of the virtualvolume can be computed by a Finite Element solver to handle the geometrical complexity of the source. As a result, it is possible to identify all the acoustic source fields at the real surface of an irregularly shaped structure and irrespective of its acoustic environment. The m-iPTF method is introduced for the first time in this paper. Conversely to the alreadypublished u-iPTF method, the m-iPTF method needs only acoustic pressure and avoids particle velocity measurements. This paper is focused on its validation, both with numerical computations and by experiments on a baffled oil pan.

International audience; Statistical modal Energy distribution Analysis (SmEdA) approach was developed to enlarge the application field of Statistical Energy Analysis (SEA) when equipartition of modal energies is not achieved. SmEdA gives more precise results than standard SEA when compared to exact energy response of a deterministic system in the case of low modal overlap, heterogeneous systems or point excitation. The present paper was initiated by this question: when considering a population of similar structures, each of them being described by SmEdA, do the ensemble averaged energies of subsystem and injected power tend to satisfy SEA equations? In other terms, despite the non-equipartition of energy observed on each element of the population of structures does the ensemble averaging leads to SEA equation where equipartition of energy is assumed? The response to that question that rises from this paper is yes, if the terms of the SEA equation are fuzzy numbers. It results that the energy response given by the model can be interpreted using fuzzy numbers theory.

National audience; L’étude du rayonnement acoustique des coques cylindriques raidies a fait l’objet de nombreux travaux car elles sont d’un grand intérêt pour les industriels des secteurs naval et aéronautique. Cependant peu d’attention a été portée aux effets liés à la présence de structures fixées rigidement à l’intérieur de la coque, telles que des planchers, des carlingages ou des supports de machines. Récemment, une méthode de sous-structuration par fonctions de transfert condensée a été développée afin de coupler un modèle de coque raidie avec des structures internes non-axisymétriques modélisées par la méthode des éléments finis. Ces travaux ont montré sur différents cas d’application numériques que la non-axisymétrie pouvait modifier significativement le comportement vibro-acoustique de la coque excitée par un effort mécanique et conduire à une augmentation de l’efficacité de rayonnement de la coque raidie. Le but de la présente étude est de vérifier ces tendances expérimentalement par des mesures en laboratoire sur une maquette. Le cylindre raidi est suspendu verticalement et est excité par un pot vibrant. La pression rayonnée est évaluée à partir de mesures en chambre anéchoïque, avec et sans structure interne. Des cartographies du champ vibratoire de la coque sont également établies à partir de mesures au vibromètre laser. L’analyse de celles-ci dans l’espace des nombres d’onde permet d’appréhender les mécanismes de rayonnement acoustique sous la fréquence critique de la coque cylindrique.

International audience; The vibroacoustic behavior of axisymmetric stiffened shells immersed in water has been intensively studied in the past. On the contrary, little attention has been paid to the modeling of these shells coupled to non-axisymmetric internal frames. Indeed, breaking the axisymmetry couples the circumferential orders of the Fourier series and considerably increases the computational costs. In order to tackle this issue, we propose a sub-structuring approach called the Condensed Transfer Function (CTF) method that will allow assembling a model of axisym-metric stiffened shell with models of non-axisymmetric internal frames. The CTF method is developed in the general case of mechanical subsystems coupled along curves. A set of orthonormal functions called condensation functions, which depend on the curvilinear abscissa along the coupling line, is considered. This set is then used as a basis for approximating and decomposing the displacements and the applied forces at the line junctions. Thanks to the definition and calculation of condensed transfer functions for each uncoupled subsystem and by using the superposition principle for passive linear systems, the behavior of the coupled subsystems can be deduced. A plane plate is considered as a test case to study the convergence of the method with respect to the type and the number of condensation functions taken into account. The CTF method is then applied to couple a submerged non-periodically stiffened shell described using the Circumferential Admittance Approach (CAA) with internal substructures described by Finite Element Method (FEM). The influence of non-axisymmetric internal substructures can finally be studied and it is shown that it tends to increase the radiation efficiency of the shell and can modify the vibrational and acoustic energy distribution.

International audience

Given the need to decrease energy consumption in the automobile industry, vehicle weight has become an important issue. Regarding acoustic comfort, the weight of noise reduction devices must be minimized inside vehicle compartments. Consequently, these devices, for example those using poro-elastic materials, must be designed carefully to maximize their influence on noise reduction. The present paper describes a method developed to obtain an efficient positioning of a given surface (or mass) of absorbing material characterized by its surface impedance. This technique is based on the Patch Transfer Function method used to couple complex vibro-acoustic sub-domains and which has been successfully applied in the European ViSPeR and Silence projects. First, a numerical analysis of the possibilities of this method is performed on a non-rectangular cavity with rigid walls after which an experimental validation of this numerical analysis is performed to evaluate the accuracy of the method under real conditions.

The present article deals with an extension of the Statistical modal Energy distribution Analysis (SmEdA) method to estimate kinetic and potential energy density in coupled subsystems. The SmEdA method uses the modal bases of uncoupled subsystems and focuses on the modal energies rather than the global energies of subsystems such as SEA (Statistical Energy Analysis). This method permits extending SEA to subsystems with low modal overlap or to localized excitations as it does not assume the existence of modal energy equipartition. We demonstrate that by using the modal energies of subsystems computed by SmEdA, it is possible to estimate energy distribution in subsystems. This approach has the same advantages of standard SEA, as it uses very short calculations to analyze damping effects. The estimation of energy distribution from SmEdA is applied to an academic case and an industrial example.

International audience; The main issue while dealing with problems due to structural vibrations is the identification of the sources that create annoyance. One of the experimental processes that permit to tackle this reverse problem uses Time Reversal method to localize the origin of the vibration detected on the surface of a structure. The Time Reversal experiment is based on a principle of time symmetry of waves propagation in a media. Using transceivers located on the structure, one can record its state of vibration. If all the signals recorded by the transceivers are reversed in time and reemitted from the position where they have been recorded, the resulting vibration will converge back to the point where it was originally emitted. In the standard approach, localization is observed both in time and space. We propose here a simplified localization process based on space localization only. We will apply this method on a complex industrial structure, stimulated with bursts. We shall show in the article the influence of certain parameters such as the number of transceivers or the structure complexity. Finally, all the tests presented hereby will allow us showing that the Time Reversal method is a very efficient and very easy to use method. (C) 2011 Elsevier Ltd. All rights reserved.

International audience; This paper proposes the intensity potential approach for prediction of high-frequency sound power radiation. The approach is based on the Helmholtz decomposition of the vector field of time-averaged sound intensity into its irrotational and rotational components. The local power balance in a lossless medium is expressed in terms of the irrotational component only, and results in the Poisson equation for a scalar intensity potential of this component only. The approach gives an exact expression for the sound power through any closed surface in terms of the irrotational component, provided that the boundary conditions are correct. The approach is evaluated by exploring the two intensity components in three canonical examples, and by comparison to measured data with special focus on directivity aspects. It is concluded that the intensity potential approach is relevant, in particular for high-frequency sound fields from multiple sources that are uncorrelated and broadbanded. However, the intensity is generally overestimated in the shadow zones and underestimated in the directly exposed regions. Further, peaks in narrow frequency bands associated with interference of waves are ignored.

International audience; The forced response of the structure-water-filled cavity system is investigated from the Patch Transfer Functions method. In such a case, a poor convergence of the PTF method is observed when using standard mode expansion to build the cavity-PTF. To improve its convergence and maintain the advantages of substructuring, residual shapes are introduced in the cavity-PTF computation, which is the new material of this article. This technique is successfully applied on numerical examples, highlighting the interest of such an approach, especially in heavy fluid.

Sound transmission through hollow structures found its interest in several industrial domains such as building acoustics, automotive industry, and aeronautics. However, in practice, hollow structures are often filled with porous materials to improve acoustic properties without adding an excessive mass. Recently a lot of interest arises for granular materials of low density that can be an alternative to standard absorbing materials. This paper aims to predict vibro-acoustic behavior of double panels filled with porogranular materials by using the patch-mobility method recently published. Biot's theory is a basic tool for the description of porous material but is quite difficult to use in practice, mostly because of the solid phase characterization. The original simplified Biot's model (fluid-fluid model) for porogranular material permitting a considerable reduction in data necessary for calculation has been recently published. The aim of the present paper is to propose a model to predict sound transmission through a double panel filled with a porogranular material. The method is an extension of a previous paper to take into account the porogranular material through fluid-fluid Biot's model. After a global overview of the method, the case of a double panel filled with expanded polystyrene beads is studied and a comparison with measurements is realized.

The aim of this paper is to demonstrate that the vibration response of systems with high modal density excited by broadband forces can be obtained by decomposing the response on a small number of effective shapes instead of a large number of mode shapes. An approach for building effective shapes on the basis of a measured mobility matrix is presented. More precisely, effective shapes can be built from eigenvectors of the space-frequency mobility matrix and a reduced model can be obtained by using only a small number of dominant eigenvectors of the SFM matrix. Systems with high modal density are characteristic of mid and high frequency problems where, for the sake of robustness, energy is often preferred to local response in order to describe the behavior of vibrating systems. The models built from the eigenvectors of the SFM matrix can be used for energy prediction and we observe that very small models are sufficient for prediction to within 3 dB. Two applications of the method are presented: the first uses numerical results in the case of longitudinal beam vibrations while the second uses experimental results obtained from plate vibrations. The method is in fact an extension of experimental modal analysis to the vibration problems of systems with high modal density.

International audience; In this article a method for calculating the radiation of plates in a thermoviscous fluid is presented. It is an extension of the plate mode expansion method used for ideal fluids to the case where thermoviscous effects are included. The model is comprehensive in the sense that it addresses all the key factors associated with thermoviscous phenomena and therefore, no simplifying assumptions are made. The influence of compressibility, inertia, viscosity, thermal conductivity and, in particular, the second coefficient of viscosity is considered. In the first part, the model is realized for an infinite plane and in the second, the model is extended towards finite simply supported plates. At the end of these mentioned sections, numerical results are provided for particular cases.

Poro-granular materials are studied, and a model adapted to characterize their acoustic behaviour is presented. Biot’s theory is used to obtain this model but a great simplification is brought to classical formulation. Indeed, a solid phase being made of a non-cohesive poro-granular material, a specific continuum constitutive model is used to characterize its behaviour. The macroscopic coefficient of friction that takes into account friction and collision phenomena is then neglected under specific conditions. This strong assumption does not apply for all kinds of granular materials and for any solicitations: its validity is discussed for particular materials. The solid/fluid model of Biot’s theory is then transformed to an equivalent fluid/fluid model. The complexity of the classical formulation is significantly reduced since only two degrees of freedom are used: the solid and fluid pressures. A 1D case is then treated to present the simplicity of the formulation, and applied to a poro-granular material made of expanded polystyrene beads. Intrinsic parameters of this material are adjusted thanks to surface impedances measured with a stationary waves tube. Finally, a study on thermal and viscous dissipations is realized and associated with a study on pressure and velocity distribution in the sample.