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In Statistical Energy Analysis (SEA) and more generally in all statistical theories of sound and vibration, the establishment of diffuse field in subsystems is one of the most important assumption. Diffuse field is a special state of vibration for which the vibrational energy is homogeneously and isotropically distributed. For subsystems excited with a random white noise, the vibration tends to become diffuse when the number of modes is large and the damping sufficiently light. However even under these conditions, the so-called coherent backscattering enhancement (CBE) observed for certain symmetric subsystems may impede diffusivity. In this study, CBE is observed numerically and experimentally for various geometries of subsystem. Also, it is shown that asymmetric boundary conditions leads to reduce or even vanish the CBE. Theoretical and numerical simulations with the ray tracing method are provided to support the discussion.

openaire: EC/H2020/727305/EU//Acoutect The tapping machine has long existed as the primary standard method for measuring the performance of floors in buildings in response to structure-borne noise. However, other sources of structure-borne noise exist. One of these is rolling noise: such as a trolley rolling across the floor in an indoor building environment. Because the sound profile of indoor rolling noise is substantially different than that of impact noise, the techniques developed to reduce the latter may not necessarily be effective at reducing the former. To this end, a means of repeatably measuring indoor rolling noise is needed. Here the results of a study on indoor rolling noise are presented, identifying the various characteristics of this type of excitation which until now have been left unexplored. The proposal for a standard rolling device is also put forth: a machine which may be capable of characterizing a floor’s performance with regards to indoor rolling noise. A series of indoor rolling noise tests were conducted in order to characterize the range of sound profiles that various indoor rolling items are capable of producing, as well as identify how the different characteristics govern the shape of the sound profile produced. Just as the standard tapping machine assesses a floor’s performance in response to impact noise, a standard rolling machine may assess a floor’s performance in response to rolling noise.

International audience; This study is concerned with the distribution of flexural vibrations in plates excited with a Gaussian white noise. The distribution of energy can be characterized by its homogeneity and isotropy. Some particular geometries like the Bunimovitch stadium generate a field that is both homogeneous and isotropic. But other geometries produce a field that is homogeneous but not isotropic (like the rectangle panel) or non-isotropic and not homogeneous (like the circular panel). It is known that these features drive the establishment of diffuse field. However, in the present work, we show that even at high frequency and for these three particular geometries, the diffuse field cannot be reached rigorously. Owing to symmetries, the vibrational response is always enhanced on some particular lines and points by the effect of coherence between rays. The enhancement factors are predicted theoretically with the image-source method. The presence of energy enhancement is also shown experimentally by measuring the vibrational energy density in the 20 Hz–4 kHz frequency range for these three plates excited with a random white noise. Measurement of enhancement factors shows a good agreement with their theoretical predictions.

International audience; Statistical modal Energy distribution Analysis (SmEdA) was developed from classical Statistical Energy Analysis (SEA). It allows computing power flow between coupled subsystems from the deterministic modes of uncoupled subsystems without assuming the SEA modal energy equipartition. SmEdA is well adapted in mid-frequency when the subsystems have not a very high modal density. However, for some systems e.g. the plate cavity system, one subsystem can exhibit a low modal density while the other one a high one. The goal of the paper is then to propose an extension of SmEdA formulation that allows describing one subsystem by its deterministic modes, and the other one supposing modal energy equipartition and a diffuse field. The uncertain subsystem is then characterized by sets of natural frequencies and mode shapes constructed based on the Gaussian Orthogonal Ensemble matrix and the cross-spectrum density of a diffuse field, respectively. This formulation permits not only the computation of mean noise response but also the variance generated by the uncertainties and furthermore without bringing in much computation. It is demonstrated that the obtained analytical results from the proposed hybrid SmEdA/SEA are consistent with that of a Monte Carol simulation which is calculated with samples having randomness in the dimension of the cavity.

This work seeks an effective data reduction method for matrices of Frequency Response Functions (FRF) in a way that preserves, as much as possible, the physical interpretation of FRFs in the full targeted frequency range. Also, this reduction method is wished able to cope with the different sources of uncertainties linked to the definition of the mechanical system whose FRFs are processed. It is shown that a Bayesian formulation of Independent Component Analysis (ICA) serves this purpose. It is used here to decompose a FRF matrix as a sum of frequency independent matrices multiplied by a frequency dependent scalar component. On the one hand, the independence property of this processing allows the scalar component to be concentrated in a narrow frequency range, on the other hand the chosen Bayesian approach presents itself as the most natural way to take into account uncertainties in the input FRFs whether they are due to measurement errors or structural uncertainties. Moreover, the probabilistic framework is shown to provide credible intervals on the estimation of the decomposition factors, thus allowing some considerations on the reliability of the processing and the development of a straightforward thresholding method to enhance the data reduction. A first application on measured automotive vibro-acoustic transfer functions shows the reduction performance of the approach and its interest when trying to analyse the measurements. A second application on non-parametric random FRFs computed through a stochastic finite element model illustrates the capacity of the proposed approach to take into account the uncertainty of the FRFs data and to propagate it to the factors of the decomposition.

This work presents a prediction model for rolling noise in multi-story buildings, such as that generated by a rolling delivery trolley. Until now, mechanical excitation in multi-story buildings has been limited to impact sources such as the tapping machine. Rolling noise models have been limited to outdoor sources such as trains and automotive vehicles. The model presented here is able to represent the physical phenomena unique to indoor rolling noise, taking into account influencing factors such as the roughness of the wheel and the floor, the material and geometric properties of the wheel and the floor, the rolling velocity of the trolley, and the load on the trolley. The model may be used as a tool to investigate how different flooring systems (including multi-layer systems) respond to rolling excitation, for the purpose of developing multi-story building solutions which are better equipped to combat this kind of noise source.

The experimental study of a structure’s response to a turbulent boundary layer (TBL) excitation using wind-tunnel or in-vehicle testing generally requires considerable efforts, including the measurement of both turbulent wall-pressure fluctuations and the structure’s vibration response. As an alternative method to highly demanding testing procedures and numerical simulations, this paper proposes a computationally efficient method to predict vibroacoustic responses of a panel under a TBL excitation. Space-time realizations of a TBL wall pressure field obtained using a spectral synthesis approach are coupled to a deterministic model so as to predict mean quadratic velocity, and radiated sound pressure and power from a panel under a TBL excitation. Each realization of the wall pressure field and obtained vibroacoustic results can be considered as a virtual experiment. The radiated sound pressure as a function of time can be also obtained, and possibly later used for listening and psychoacoustics studies objectives. A summary of existing experimental and numerical methods for obtaining the vibroacoustic response of panels to a TBL excitation is first presented. The proposed method is then detailed. Results obtained using this method are finally compared to results obtained using controlled laboratory experiments and analytical calculations for a low subsonic flow speed.

International audience; In vehicle tire/road contact modeling, dynamic models are typically used which incorporate the vehicle's suspension in their estimation: thus relying on a known stiffness to determine the movement of the wheel in response to roughness excitation. For the case of a wheeled device rolling on a floor (such as a delivery trolley moving merchandise around inside a commercial building), there is often no suspension, yet the wheel is still too soft to able to be considered mechanically rigid (as is the case in train/rail contact). A model which is aimed at incorporating the dynamic effects of the trolley in predicting the sound generated by rolling needs to provide a robust way of estimating the wheel's effective stiffness. This work presents an original technique for estimating the stiffness of a solid cylindrical wheel. A parametric study was conducted in order to identify the dependence of the wheel stiffness on each of the relevant variables: including the wheel's radius, axle size, width, applied load, and material properties. The methodology may be used to estimate the stiffness of new wheel types (i.e. different geometries and materials) without needing to solve a finite element model each time. Such a methodology has application beyond the field of acoustics, as the characterization of shapes with nonconstant cross sections may be useful in the wider field of materials science.

International audience; In the field of acoustic source reconstruction, the inverse Patch Transfer Function (iPTF) has been recently proposed and has shown satisfactory results whatever the shape of the vibrating surface and whatever the acoustic environment. These two interesting features are due to the virtual acoustic volume concept underlying the iPTF methods. The aim of the present article is to show how this concept of virtual subsystem can be used in structures to reconstruct the applied force distribution. Some virtual boundary conditions can be applied on a part of the structure, called virtual testing structure, to identify the force distribution applied in that zone regardless of the presence of other sources outside the zone under consideration. In the present article, the applicability of the method is only demonstrated on planar structures. However, the final example show how the method can be applied to a complex shape planar structure with point welded stiffeners even in the tested zone. In that case, if the virtual testing structure includes the stiffeners the identified force distribution only exhibits the positions of external applied forces. If the virtual testing structure does not include the stiffeners, the identified force distribution permits to localize the forces due to the coupling between the structure and the stiffeners through the welded points as well as the ones due to the external forces. This is why this approach is considered here as a selective structural source identification method. It is demonstrated that this approach clearly falls in the same framework as the Force Analysis Technique, the Virtual Fields Method or the 2D spatial Fourier transform. Even if this approach has a lot in common with these latters, it has some interesting particularities like its low sensitivity to measurement noise.

Current approaches in the automotive domain to predict booming noise essentially target extreme loading conditions. This is useful when mechanical strength is of concern, but not representative of the actual vehicle usage. Usage is however important when addressing acoustic annoyance. One issue in this respect is the lack of databases representative of the diversity of client usages and, therefore, of the excitation forces applied to the vehicle in real usage conditions. This paper introduces a possible answer to this problem. First, it proposes a measurement protocol to estimate the excitation forces in real usage responsible of booming noise. Second, it provides an array of algorithms to analyze the large amount of data collected during the measurement step. In particular, an ad hoc Independent Component Analysis algorithm is introduced to extract excitation components specific to well-defined operating condition regions, thus providing insights in the excitation behaviour, as well as data reduction. Next, the excitation components are modelled as a function of the vehicle operating conditions with a Radial Basis Function network. A meta-model of the excitations in real usage conditions is thus obtained, composed of two levels: the analysis level and the modelling level. The proposed methodology is developed in the Bayesian framework. In addition to its advantages linked to the trivial introduction of prior knowledge, the Bayesian framework is found particularly useful for propagating uncertainties throughout the successive steps of the approach.

MODal ENergy Analysis (MODENA) was previously developed in the same framework as Statistical Energy Analysis (SEA) and Statistical modal Energy distribution Analysis (SmEdA) methods. It deals with energy exchanges between weakly coupled subsystems in vibro-acoustics. However, unlike SEA, MODENA is not a statistical method as it is based on deterministic structures and solved at pure tone. Compared to SmEdA, MODENA takes intrinsically into account couplings between non resonant modes and keeps information about resonance peaks. Consequently, it handles matrices of bigger size than SmEdA with the consequence of higher computation cost. MODENA was first based on the assumption of uncorrelated forces applied to two coupled oscillators. This assumption was fulfilled by considering a random phase between forces applied to oscillators. In the present article, this assumption is further investigated by considering the phase angle as a random variable with uniform distribution. The expressions for expectation and variance are then derived in this context. They allow estimating confidence intervals of energies predicted by MODENA method. Therefore, even if the assumption of random phase is not fulfilled, the solution should be included in the confidence interval. It is shown that confidence intervals of energies are rather null in case of two weakly coupled oscillators both excited by forces of equivalent level. The confidence intervals increase at some frequencies when the coupling strength is higher than the critical coupling or when the excitation level difference increases. In case of multi-modal coupling, two numerical test cases are investigated: a plate/cavity case and a cavity/plate/cavity case. In both cases, expectations and variances are computed using MODENA theory and are compared to deterministic responses of the subsystems computed using a finite element software.

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; With the aim of decreasing CO2 emissions, car producers’ efforts are focused, among others, on reducing the weight of vehicles yet preserving the overall vibrational comfort. To do so, new lightweight materials combining high stiffness and high (passive) damping are sought. For panels essentially loaded in bending, sandwich composites made of two external metallic stiff layers (skins) and an inner polymeric (i.e. absorbing) core are broadly used. Now aiming at creating materials by design with a better control of the final performance of the part, the tuning of the local material properties is pursued. To this end, the present work focuses on controlling the spatial in-plane viscoelastic properties of the polymeric core of such sandwich structures. The spatial patterning is achieved using a recently developed UV irradiation selective technique of Room Temperature Vulcanization (RTV) silicone elastomeric membrane, in which the ultraviolet (UV) irradiation dose, curing time and temperature are the process parameters controlling the viscoelastic properties of the polymeric membrane. Finally, a protocol for the realization of architected aluminum - silicone - aluminum composite sandwich panels is proposed. The influence of UV irradiation selective technique is demonstrated by Dynamic Mechanical Analysis (DMA) measurements on the silicone core itself and by the Corrected Force Analysis Technique (CFAT) to measure the equivalent Young’s modulus and damping of the sandwich structure over a large frequency band. As a first demonstration application, sandwich beams with different core patterns (homogeneous and heterogeneous) are designed and tested. Furthermore, the analytical formalism developed by Guyader et al. is used to model the vibro-acoustic performances of the homogenous sandwich beams and fair model-experiments comparisons are obtained. The spatial patterning of the polymer layer is found to successfully affect the local properties of the composite heterogeneous beam as evidenced by the CFAT method. Finally, this work permits the enunciation of guidelines for designing complex architectured systems with further control of the vibro-acoustics performances.

International audience

The workshop is partly supported by the LMAc institute, Le Mans Acoustique. This symposium is an action of the "METAPLAQ" research project funded over the period 2016-2019.; International audience; Since 2014 several collaborations between two laboratories of INSA Lyon - Mateis (materials science) and LVA (vibroacoustics) - have been focused on the modeling, designing and measuring hybrid sandwich composites structures with optimized damping properties for given frequency domains. The proposed contribution gives an overview of these modeling and experimental efforts, by presenting some results on several application cases.In a first study ([1-4]), a three layer steel/polymer/steel plate sandwich system is considered. Several aspects are studied by comparing four measurement techniques and three analytical models predictions. High resolution modal analysis coupled to contactless measurement of the velocity field of plates (CFAT) leads to the estimation of the equivalent single layer complex rigidity (frequency dependent “apparent bending stiffness” and “apparent damping”) for the whole [40Hz-20kHz] frequency band. Compared to the analytical modelling of Guyader based on wave propagation analysis, the results are in very good agreement. The comparison with this theoretical approach allows identifying the frequency dependent complex modulus of the polymer core layer through inverse resolution. The predicted properties turned out to match DMA measurements performed on the polymer material alone and the associated high frequency predictions (using the time-temperature equivalence principle). With this approach, the design of multilayer plates for vibroacoustics applications with optimized damping properties for given frequency domains may be performed.The second study ([5,6]) focuses on controlling the spatial in-plane viscoelastic properties of the polymeric core of sandwich structures. Aiming at creating materials by design, the tuning of the in-plane local material properties is pursued. The spatial patterning is achieved using a recently developed UV irradiation selective technique of Room Temperature Vulcanization silicone elastomeric membrane. “Structured” three-layer beams (aluminum/silicon/aluminum) with different core patterns (homogeneous and heterogeneous) are designed and tested. Fair model-experiments comparisons are obtained. This work permits the enunciation of guidelines for designing complex architectured systems with further control of the vibro-acoustics performances. In particular the effect of the viscoelastic patterning on the “optimum shearing zone” (position and width) will be discussed. The explored material solutions could be dedicated from low to very low frequency ranges where meta-material-based solutions are often inefficient.1.Ege et al., Inter-Noise 2015, San Francisco2.Roozen et al., JSV 2017, 390, pp.257-271. 3.Roozen et al., JSV 2017, 395, pp.90-101.4.Ege et al., JSV 2018, 426, pp.129-149.5.Gallo et al., Acoustics'2017, Boston.6.Gallo et al., ISNVH 2018, Graz.

National audience; Respecter les normes pour la lutte contre la pollution des véhicules et leurs nuisances sonores est l’un des enjeux majeurs de ces dernières années pour l’industrie du transport. Cette problématique a poussé à alléger les véhicules en remplaçant les matériaux métalliques par de nouveaux matériaux conservant de bonnes performances de résistance mécanique et d’isolation vibroacoustique. Dans cette optique, un nouveau procédé de matériaux multicouches a été développé. L’assemblage est constitué d’une âme en polymère (silicone) placée entre deux peaux métalliques. Les propriétés mécaniques du silicone sont contrôlées par irradiation UV à l’aide de masque intercalés entre la source UV et le matériau silicone permettant de contrôler localement les propriétés du polymère (module d’Young et facteur de perte) et de créer ainsi un matériau multicouches architecturé.Nous abordons dans la première partie de cet article une étude analytique (modèle de Guyader, JSV 1978) qui porte sur les différences de propriétés mécaniques qui existent entre deux poutres multicouches spatialement homogènes irradiée et non irradiée et nous en présentons la validation expérimentale. Pour cela, la méthode RIFF (Résolution Inverse Filtrée Fenêtrée) est utilisée. Elle permet d’identifier les propriétés mécaniques du matériau spatialement et en fonction de la fréquence. Pour vérifier le contrôle local du module d’Young grâce au procédé d’irradiation, une troisième poutre multicouches similaire aux précédentes, mais dont l’âme est composée d’un silicone dont l’irradiation varie sur sa longueur, est ensuite étudiée. Enfin, quelques exemples d’architecturation des propriétés du multicouches sont présentées à l’aide de modèles éléments finis.

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 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.

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 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.

In order to design vehicles with diminished CO2/km emissions level, car manufacturers aim at reducing the weight of their vehicles. One of the solutions advocated by the automotive engineers consists in the replacement of metallic parts by lighter systems made of polymer composites. Unfortunately, the numerical simulations set to evaluate the vibratory and acoustic performances of systems made of this kind of materials are often not sufficiently effective and robust so that convincing test/simulation correlations are rarely met. Indeed, for polymer-based materials, numerous parameters affect the vibroacoustic behavior of the system. For the present study, focusing on Polyamide 6 reinforced glass fiber plates (PA6-GF35), it will be demonstrated using DMA (Dynamic Mechanical Analysis) and FAT (Force Analysis Technique) analysis that the viscoelastic properties depend on the temperature and frequency but also on the humidity content. We will compare the FAT method which permits to identify the equivalent com...

International audience; With the aim of decreasing CO2 emissions, car producers’ efforts are focused, among others, on reducing the weight of vehicles yet preserving the overall vibrational comfort. To do so, new lightweight materials combining high stiffness and high (passive) damping are sought. For panels essentially loaded in bending, sandwich composites made of two external metallic stiff layers and an inner polymeric (i.e. absorbing) core are broadly used. In the present work, the performances of such sandwich structures are enhanced by optimizing their damping behavior according to their use. More precisely, spatial patterning through selective UV irradiation of the viscoelastic properties of the silicone elastomeric layer is obtained based on a recently published UV irradiation selective technique [1]. Initially developed to modulate the elastic property gradient in Liquid Silicone Rubber (LSR) membranes, the procedure is now generalized to control the viscoelastic behavior of Room Temperature Vulcanization (RTV) silicone. Since the Young’s modulus and damping factor of the polymeric material are triggered by the UV irradiation dose, the resulting vibration response of the sandwich composite, made of aluminum skins and RTV silicone core, can be accordingly tuned. [1] Stricheret al. (2016). “Light‐Induced Bulk Architecturation of PDMS Membranes,” Macromol. Mater. Eng. 301(10), 1151-1157.

International audience; This paper is a discussion of the hypothesis of weak coupling in statistical energy analysis (SEA). The examples of coupled oscillators and statistical ensembles of coupled plates excited by broadband random forces are discussed. In each case, a reference calculation is compared with the SEA calculation. First, it is shown that the main SEA relation, the coupling power proportionality, is always valid for two oscillators irrespective of the coupling strength. But the case of three subsystems, consisting of oscillators or ensembles of plates, indicates that the coupling power proportionality fails when the coupling is strong. Strong coupling leads to non-zero indirect coupling loss factors and, sometimes, even to a reversal of the energy flow direction from low to high vibrational temperature.

The characterisation of the aeroacoustic wall pressure field generated by turbulent flow is a difficult task that often requires instrumented panels and huge facilities like wind tunnels. In situ and non-intrusive experiments are rather not possible. In addition, the pressure field is dominated by the aerodynamic component and the experimental dynamics are not sufficient to measure correctly spectra in low wavenumbers by microphones. The present chapter deals with such a separation method by using the Force Analysis Technique (FAT). FAT is based on the use of the equation of motion of the structure (here a plate) and on the approximation of the fourth derivatives by a finite difference scheme. In the case of turbulent flow, the force auto-spectrum can be deduced at one point of the structure by measuring the velocity at 13 points synchronously. To this purpose, an array of 13 pU (acoustic pressure/particle velocity) probes has been made up. This array is moved in the near-field of the plate to identify map of the wall pressure level applied on the surface of the plate. In the present application, it is shown that FAT only identifies the component of the excitation with wavenumber lower than the natural flexural wavenumber of the plate, due to filtering effect of the plate and of the finite difference scheme. In most cases, the convective peak is then canceled and only the acoustic part of the turbulent flow is identified. This property can be of great interest for vehicle manufacturers to quantify the part of the wall pressure that is responsible of the radiated noise or to use FAT as a source separation technique.

International audience; The City Lightweight and Innovative Cab (CLIC) project is a scientific collaboration gathering different public and private organizations. The aim is to propose an innovative truck cab responding to new European legislations in security and CO2 emission. A very high strength steel will be used to lighten the structure. This could affects directly the acoustic environment of the cab. In order to control the noise requirements at the design stage, it is then necessary to be able to simulate the vibroacoustic behavior of a truck cab in the mid frequency range. In this context, a methodology is developed at INSA Lyon based on Statistical modal Energy distribution Analysis (SmEdA). This method is considered as substructuring approach for vibroacoustic problems and post-process for finite element methods (FEM). It is based on the knowledge of the uncoupled subsystem modes that can be computed using the FEM. In this paper, one focuses on the fluid-structure coupling of the cab floor with the interior cavity when they are represented by non-coincident meshes.

International audience; City Lightweight Innovative Cab (project CLIC) aims at developing a new generation of lightweight trucks. Mass reduction of a structural body may necessitate extensive use of additive damping mechanisms. Statistical Modal Energy Distribution Analysis (SmEdA) can be used to analyze the energy transmission of a structure-cavity system in the mid-high frequency domain. In this paper, the methodology is extended to take into account the effect of dissipative materials applied to each subsystem. This includes a characterization of the damping material as an equivalent property of treated subsystems, which greatly reduces a size of a finite element system to be solved and leads to a more efficient numerical implementation.

National audience; Statistical modal Energy distribution Analysis (SmEdA) can be used to model a fluid-structure-problem based on modal information of the uncoupled-subsystems. Recently the method has been extended to include the effect of a dissipative treatment (i.e. damping or absorbing material). In this paper, SmEdA is tested on a steel plate with/without damping treatment coupled to an acoustic cavity: the numerical result of the energy ratio is compared to the experimental one The data are analyzed for a mid-to-high frequency domain (up to 10 kHz in 1/3 octave band). Both subsystems loss factors are experimentally obtained by a high-resolution modal analysis method based on the ESPRIT algorithm applied to impulse responses of the plate and the cavity. Predicting the energy level requires an accurate estimation of subsystem damping levels. The uncertainty on measured loss factors leads to an uncertainty in the energy ratio depending on min/max damping levels of individual modes in a given frequency band. Once min/max damping levels of subsystems are determined, SmEdA is used to compute the upper and lower limit of the subsystem energy ratio. Comparison with the experiment shows that the measurement data fits in between the SmEdA bounds. In this paper, two types of dissipative treatments are studied: i) a viscoelastic patch on the plate (modeled as an equivalent single layer plate) and ii) a porous material into the cavity (modeled as an equivalent fluid).

Statistical modal Energy distribution Analysis (SmEdA) can be used as an alternative to Statistical Energy Analysis for describing subsystems with low modal overlap. In its original form, SmEdA predicts the power flow exchanged between the resonant modes of different subsystems. In the case of sound transmission through a thin structure, it is well-known that the non resonant response of the structure plays a significant role in transmission below the critical frequency. In this paper, we present an extension of SmEdA that takes into account the contributions of the non resonant modes of a thin structure. The dual modal formulation (DMF) is used to describe the behaviour of two acoustic cavities separated by a thin structure, with prior knowledge of the modal basis of each subsystem. Condensation in the DMF equations is achieved on the amplitudes of the non resonant modes and a new coupling scheme between the resonant modes of the three subsystems is obtained after several simplifications. We show that the contribution of the non resonant panel mode results in coupling the cavity modes of stiffness type, characterised by the mode shapes of both the cavities and the structure. Comparisons with reference results demonstrate that the present approach can take into account the non resonant contributions of the structure in the evaluation of the transmission loss., Comment: Journal of Sound and Vibration (2013) - Article in press - http://dx.doi.org/10.1016/j.jsv.2013.09.007

International audience; Energy methods like Statistical Energy Analysis (SEA) or Statistical modal Energy distribution Analysis (SmEdA), based on the well-known equations of two coupled oscillators, are both limited when non-resonant contributions of modes are not negligible (typically in the case of cavity/structure/cavity coupling). In SEA, this non-resonant contribution can be taken into account introducing indirect coupling between subsystems. In SmEdA, the nonresonant contribution is more difficult to estimate as indirect coupling is not allowed. However, this issue can be a matter of importance to compute Transmission Loss (TL) of highly damped structures for example. The present work deals with an energy method, developed within the framework of SmEdA, which solves the system of equations of two coupled oscillators at pure tone, taking thus intrinsically into account the non-resonant contributions of oscillators. As in SEA or SmEdA, the net exchanged power between two coupled oscillators is proportional to the weighted difference of total energies of oscillators. The expression of a critical coupling strength is also proposed and may be related to classical weak coupling criterion of SEA. Extending equations obtained for two coupled sets of oscillators to the case of two linear continuous subsystems, one can compute easily frequency dependent modal energies of modes, total energies of subsystems, power transmitted between two modes and power dissipated. The theoretical bases and assumptions of the proposed MODal ENergy Analysis (MODENA) are first exposed and the case of two coupled oscillators is addressed. Then, plate/cavity and cavity/plate/cavity systems are treated with MODENA and compared to an exact solution. Finally, it is demonstrated that the non-resonant contribution of a highly damped plate is correctly represented by MODENA.

International audience

International audience

International audience; In noise control, identification of the source velocity field remains a major problem open to investigation. Consequently, methods such as nearfield acoustical holography (NAH), principal source projection, the inverse frequency response function and hybrid NAH have been developed. However, these methods require free field conditions that are often difficult to achieve in practice. This article presents an alternative method known as inverse patch transfer functions, designed to identify source velocities and developed in the framework of the European SILENCE project. This method is based on the definition of a virtual cavity, the double measurement of the pressure and particle velocity fields on the aperture surfaces of this volume, divided into elementary areas called patches and the inversion of impedances matrices, numerically computed from a modal basis obtained by FEM. Theoretically, the method is applicable to sources with complex 3D geometries and measurements can be carried out in a non-anechoic environment even in the presence of other stationary sources outside the virtual cavity. In the present paper, the theoretical background of the iPTF method is described and the results (numerical and experimental) for a source with simple geometry (two baffled pistons driven in antiphase) are presented and discussed.

National audience; La mesure directe du champ de pression pariétale généré par une couche limite turbulente (CLT) sur une structure requiert l'utilisation de microphones affleurants ou déportés, nécessitant une paroi instrumentée spécifique. Une estimation indirecte de ce type d'excitation pourrait permettre de s'affranchir de l'instrumentation de la paroi. La méthode RIFF (pour Résolution Inverse Filtrée Fenêtrée) est une méthode de mesure permettant d'estimer la pression appliquée localement à une structure de type plaque à partir de mesures de sa réponse vibratoire. Cette méthode est basée sur une approximation par différences finies de l'équation du mouvement et nécessite uniquement la mesure en 13 points rapprochés de la réponse de la structure pour obtenir la pression en 1 point central. Une mise en œuvre expérimentale dans un tunnel aérodynamique a été réalisée pour évaluer l'applicabilité de la méthode RIFF aux structures sollicitées par une CLT. La pression pariétale générée à l'arrière d'un obstacle situé dans le flux a été mesurée directement par une antenne de microphones et indirectement par RIFF à l'aide d'une antenne de 13 capteurs de vitesse acoustique positionnée très proche de la plaque vibrante à l'extérieur du tunnel. Les résultats obtenus mettent en évidence un effet de filtrage spatial de la méthode RIFF où la question de la possibilité d'identifier la part acoustique du champ excitateur est discutée.

International audience

International audience

National audience; On s'intéresse dans cet article à la modélisation du couplage entre une structure et une cavité d'eau pour des fréquences situées en dessous de la fréquence critique de la structure. Ce type de problème se caractérise par le fait que : (a), le couplage entre la structure et le fluide est fort ; (b), le rayonnement de la structure fait apparaître des ondes évanescentes qu'il est difficile de reproduire à partir de séries modales. Ce problème a été traité dans de nombreuses publications et peut être résolu à partir de méthodes numériques telles que les éléments finis, les éléments finis de frontière, les éléments infinis, etc. Les temps calculs deviennent cependant très vite prohibitifs dès que la fréquence augmente. Pour les réduire, on propose de sous-structurer le problème vibro-acoustique à partir de l'approche PTF (Patch Transfert Functions). Celle-ci consiste à décomposer le système en différents sous-domaines et à découper les surfaces de couplage en pavés Des fonctions de transfert par pavés caractérisent alors les sous-domaines. Celles-ci peuvent être calculées par différentes méthodes sur les sous-domaines découplés. Elles servent ensuite à reconstituer la réponse du système global à partir des équations de continuité, qui ne font pas intervenir d'hypothèse sur la nature du couplage entre les sous-systèmes. Il est donc possible de sous-structurer le problème de différentes façons. Nous allons ainsi étudier différentes sous-structurations du problème ainsi que différentes techniques de calcul des fonctions de transfert par pavé, ceci dans le but de minimiser les temps de calcul.

International audience; Reliability of statistical energy analysis (SEA) models depends on good estimates of coupling loss factors (CLFs), modal densities, and damping loss factors. Statistical modal energy distribution analysis (SmEdA), a finite element based method to compute CLFs from uncoupled finite elements models of subsystems, is used to generate SEA CLF for general subsystems. This method is based on the basic SEA relations for coupled oscillators and on a dual modal formulation to describe the vibration of coupled subsystems. Previous works have demonstrated the use of the SmEdA method for structureto- structure couplings. The current work extends the SmEdA process to structure-tocavity couplings. The estimation of CLF using the SmEdA approach is compared, for a simple test case, to analytical results and a classical expression obtained with a wave approach. Results show good comparison with analytical results even below critical frequency, where the wave approach underestimates CLF. Finally, an industrial application has been carried out to demonstrate that the SmEdA approach can be used in the case of complex structures.

This study presents a method of using acoustic holography and the force analysis technique to identify vibration sources from radiated noise measurements. The structure studied is a plate excited by a shaker on which three measurements were performed: the first is a reference measurement of plate velocity obtained by scanning laser vibrometry, the second is based on sound pressure measurements in the near field of the structure, and the third is the measurement of normal acoustic velocities by using a p-U probe recently developed by Microflown Technologies. This was followed by the application of classical NAH, known as pressure-to-velocity holography and velocity-to-velocity holography to predict the plate velocity field from acoustic measurements at distances of 1 and 5 cm. Afterwards, the force analysis technique, also known as the RIFF technique, is applied with these five data sets. The principle is to inject the displacement field of the structure into its equation of motion and extract the resulting force distribution. This technique requires regularization done by a low-pass filter in the wavenumber domain. Apart from pressure-to-velocity holography at 5 cm, the reconstructed force distribution allows localizing the excitation point in the measurement area. FAT regularization is also shown to improve results as its cutoff wavenumber is optimized with the natural wavenumber of the plate. Lastly, quantitative force values are extracted from force distributions at all frequencies of the band 0–4 kHz studied and compared with the force spectrum measured directly by a piezoelectric sensor.

International audience

On one hand, energy methods usually deal with frequency averaged quantities. Statistical Energy Analysis, for example, uses energy per subsystems and power injected averaged over frequency bands. On the other hand, when a structure is excited by a turbulent boundary layer, its response is calculated using a model of boundary pressure cross spectrum (Corcos, Efimtsov...). Such calculations take into account boundary conditions and exact geometry of the excited structure which is often non necessary for energy methods. A model of Frequency Averaged Injected Power under boundary layer excitation (FAIP model [1]) has been previously proposed as a tool for vibroacoustic pre-design process. The present paper deals with an experimental validation of the FAIP model. To validate this approach, a characterization of the turbulent flow (wall pressure spectrum, velocity profiles, correlation lengths, Corcos' coefficients) have been carried out in the wind tunnel of the Ecole Central of Lyon. In a second step, the power injected into a plate placed onto a dedicated setup has been evaluated measuring the velocity field on the plate with a laser vibrometer. Thus, experimental power injected into the plate has been compared with the one predicted by FAIP model. FAIP model are in good agreement with Experiments showing that FAIP model is able to give accurate estimation of power injected into a plate excited by a turbulent boundary layer (TBL) on the whole frequency range (below, above and at the aerodynamic coincidence frequency). Four plates made in different materials (steel, copper, PVC) and of different geometries have been tested for three free stream velocities (20, 35 and 50 m/s).

International audience