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In recent years, acoustic black holes (ABHs) exhibit fascinating damping effects at mid-to-high frequencies. However, flexural waves having long wavelength cannot be trapped in the ABH pit when there is a residual thickness at the ABH tip, therefore below the cut-on frequency the ABH effect fails to work. While locally resonant acoustic metamaterials allows mitigating vibrations in subwavelength scale, usually in a narrow band. In this paper we combine the advantages of the metamaterials and ABHs (MMABH) to control vibrations in the whole frequency band. The designed MMABH plate remains the same weight to the reference uniform plate. To characterize the MMABH performance, an artificial spring component mode synthesis (GECMS) method is suggested, based on the modal coupling between the resonators and the ABH plate via springs. The band gap for the infinite periodic MMABH and the modes for the finite MMABH have been accurately predicted with the GECMS, compared to a reference FEM model. Numerical results show that the low-frequency peaks of the ABH plate can be substantially suppressed when the resonators with proper loss factor are set at its first resonant frequency. The proposed MMABH shows great potentials for light-weight and whole-band vibration reduction.

In recent years, acoustic black holes (ABHs) have been shown very effective to suppress radiation. However, below the cut-on frequency, the waves cannot be trapped into the ABH. In this paper, locally resonant metamaterials are introduced to the ABH plate to improve the low-frequency performance. The suggested material is called MMABH. The total mass of resonators is kept the same to the one when fabricating the ABH, such that the lightweight feature still remains valid for the MMABH. Using the Gaussian expansion component mode synthesis (GECMS) method, the band gap and the coincidences between the MMABH and the air are first characterized, together with the paramagnetic studies of the plate thickness and lattice constant. In what follows, the vibration field of the MMABH is recovered, showing that whole-band reduction can be achieved. The sound pressure, power and radiation efficiency are next characterized via a discretized radiation model. Likewise, the radiated power is substantially mitigated in the whole frequency range being considered. Finally, the implementation of non-negative intensity (NNI) shows that the sound reduction not only associates with the outstanding damping capabilities of the resonators and the ABH, but also involves the wave slowdown phenomenon that breaks the coupling with air.

In this paper, a numerical process is presented for predicting the response of vibrating structures excited by a non-homogeneous turbulent boundary layer. This one is based on the synthesis of different realizations of the random pressure fluctuations that can be introduced as loading of a vibroacoustic model. The vibratory response is finally deduced by averaging together the responses of the different loads. As a first approach, the pressure fluctuations of the non-homogeneous turbulent boundary layer can be generated separately for different sub-areas of the structure by using the uncorrelated wall plane waves technique and mean boundary layer parameters. An extension of this basic approach consists in taking into account the interaction between the sub-areas and a refinement of the sub-area decomposition. Wall pressure fluctuations related to a continuous evolution of the boundary layer can then be generated and introduced in the vibroacoustic model. The accuracy of the proposed approach is studied on a rectangular panel excited on one side by a growing fully turbulent boundary layer triggered at one edge of the plate. Comparisons with the spatial approach and the wavenumber approach using the sub-area decomposition technique are proposed. Interests of the proposed approach in terms of accuracy and computing times are discussed.

Embedding acoustic black holes (ABHs) on beams and plates has revealed as an appealing passive method for noise and vibration reduction. However, most ABH designs to date only concern straight beams and flat plates, while cylindrical structures are commonly found in the aeronautical and naval sectors. In this work, we suggest a semi-analytical method to compute the vibration field of a cylinder with an ABH indentation. We also show the ABH efficiency in terms of shell vibration reduction. It is proposed to resort to Gaussian basis functions in the framework of the Rayleigh-Ritz method, to reproduce the ABH cylinder vibration field. The ABH shell displacements in the three directions are decomposed in terms of Gaussian functions, which can be dilated and translated analogously to what is done with wavelet transforms. The functions are also forced to satisfy the continuity periodic conditions in the shell circumferential direction. The Gaussian expansion method (GEM) results in high precision at a low computational cost. The suggested semi-analytical method is validated against a detailed finite element (FEM) model. Modal frequencies and modal shapes are recovered very accurately. Besides, the mean square velocity of the annular ABH shell under point external excitation is compared to that of a uniform shell, in the 50-1000 Hz frequency range. Noticeable vibration reduction is achieved.

Decoupling procedures based on substructuring methods allow to predict the vibroacoustic behaviour of a given system by removing a part of an original system that can be easily modelled. The reverse Condensed Transfer Function (rCTF) method has been developed to decouple acoustical or mechanical subsystems that are coupled along lines or surfaces. From the so-called condensed transfer functions (CTFs) of the original system and of the removing part, the behaviour of the system of interest can be predicted. The theoretical framework as well as a numerical validation have been recently published. In the present paper, we focus on the influence of numerical errors on the results of the rCTF method, when the CTFs are calculated using numerical models for the original system and/or the removed part. The rCTF method is applied to a test case consisting in the scattering problem of a rigid sphere in an infinite water domain and impacted by an acoustic plane wave. Discrete green formulation and finite element method are used to estimate the CTFs. Numerical results will be presented in order to evaluate the sensitivity of the method to model errors and the potential promises and limitations of the method will be highlighted.

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.

Ce chapitre propose des exemples de méthodes « hybrides », adaptées à la modélisation et la simulation de problèmes vibro-acoustiques dans le domaine des « moyennes fréquences ». L’objectif de ces méthodes est d’obtenir, à moindre de coûts de calcul, des résultats déterministes et locaux, utiles aux ingénieurs afin d’estimer des niveaux de bruits rayonnées par des structures navales.

An analytical framework for sound radiation from a fluid-loaded cylindrical shell covered with an acoustic coating is presented. The coating is composed of a soft elastic material embedded with a circumferential layer of equispaced voids. The layer of voids is modeled as an effective fluid medium sandwiched between two layers of the host material. Expressions for the effective impedance of the coating, radial displacement of the elastic shell, and the structure-borne radiated pressure for harmonic excitation of the shell are derived. Results show that the coating design can be tuned to reduce the radiated sound in a broad frequency range.

International audience; This study concerns a monitoring technique based on vibration measurements for identifying the presence of an acoustic source in a fluid-filled pipe conveying turbulent flow. In such situation, the source-induced vibrations can be smeared with the flow-induced vibrations, which hinders detecting the presence of the source. To increase the signal-to-noise ratio (SNR), beamforming techniques can be applied to the vibrations measured by an array of accelerometers mounted on the pipe. However, the current problem is more complex and challenging than most typical beamforming applications due to strong fluid-structure coupling and to the presence of resonant modes and internal flow excitations. Numerical vibroacoustic methods are presented to predict the vibratory response of a pipe excited by a monopole source and/or a turbulent boundary layer (TBL). The cross-spectral matrices of the computed radial accelerations induced by the monopole source to be detected and by the TBL are used for assessing the performance of two vibroacoustic beamforming techniques. The array gains using both, the conventional and the MaxSNR beamforming approaches are estimated. Results indicate superior performance of the MaxSNR, which leads to significantly higher array gain.

In this paper, a numerical method is presented to predict the vibroacoustic response of a vibrating structure excited by a spatially inhomogeneous turbulent boundary layer. It is based on the synthesis of different realizations of random pressure fluctuations that can be introduced as loadings of a vibroacoustic model (such as a finite element model). The vibro-acoustic response is finally deduced by averaging the responses for the different loads. To generate the pressure fluctuations of the non-homogeneous turbulent boundary layer, the Uncorrelated Wall Plane Wave (UWPW) approach used so far for homogeneous boundary layers is extended. On a first step, this extension is based on a decomposition of the excited surface into sub-areas and on the averaged parameters of the boundary layer on each sub-area. In a second step, it consists in considering the interaction between the sub-areas and a refinement of the sub-area decomposition. This leads to the Continuously-varying Uncorrelated Wall Plane Waves (C-UWPW) approach. The accuracy of the proposed approach is investigated on a rectangular panel of variable thickness and excited by a growing turbulent boundary layer triggered at one edge of the plate. Comparisons with the spatial approach, usually used but with very long computation times, are presented. The interests of the proposed approach in terms of accuracy and computation time are discussed. An illustration of the proposed approach to predict the radiated noise from a blade immersed in a water flow will be proposed during the oral presentation.

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; The reproduction of the vibration and acoustic responses of structures under random excitation such as the diffuse acoustic field or the turbulent boundary layer is of particular interest to researchers and the transportation industry (automobile, aeronautics, etc.). In practice, the characterization of structures under random excitations requires making in-situ measurements or using test facilities such as the wind tunnel, which are complex and costly methods. Based on the previous considerations, the necessity of finding simple, cost-efficient and reproducible alternative methods becomes obvious. The source scanning technique based on a single acoustic source and the synthetic array principle is one of these alternative techniques. The present paper proposes to assess its validity by comparing its results with numerical and experimental ones. An academic case study consisting of a baffled and simply supported aluminum panel under diffuse acoustic field and turbulent boundary layer excitations is considered. The experimental vibration response of the panel as well as the transmission loss using the proposed process are compared to results from random vibration theory on one hand. On the other hand, the same experimental results obtained using the source scanning technique are compared with results obtained with measurements using a reverberant room (diffuse acoustic field) and an anechoic wind tunnel (turbulent boundary layer). These comparisons show good agreement that validate the source scanning technique for the considered panel.

A vibro-acoustic model of a structurally excited cylindrical shell of infinite length submerged in a heavy fluid at a finite distance from a free surface is presented. Expressions for the shell displacement, the acoustic pressure in the interior cavity of the shell and the acoustic pressure at all field locations in the exterior domain are analytically derived. The formulation for the exterior acoustic pressure is developed using the image method and Graf's addition theorem. Results for the structural and acoustic responses of the cylindrical shell submerged at a finite distance from the free surface and in an unbounded fluid domain are compared. The effects of the shell circumferential modes, interior cavity resonances and proximity of the free surface on the shell acoustic responses are examined. New mechanisms influencing the low frequency vibro-acoustic response of a submerged hull near a fluid boundary are described.

Annular acoustic black holes (ABHs) have been recently proposed as a potential means for reducing vibrations of cylindrical shells. The latter are very common structures in the naval, aeronautic and industrial sectors so widening ABH applications from flat plates to curved structures seems worth exploring. This work focuses on the benefits of embedding annular ABH indentations on cylindrical shells to reduce outward sound radiation. The goal of the paper is to propose a semi-analytical method to determine the acoustic power, radiation efficiency, source location and far-field acoustic pressure of ABH shells and compare them with those of uniform thickness shells. The vibration field of the ABH and uniform cylindrical shells is computed by means of the Gaussian expansion method (GEM) within the Rayleigh–Ritz approach. Then, the radiated pressure is obtained by solving the Helmholtz equation in cylindrical coordinates using the Green’s function method. The surface of the cylinder is discretized into small finite size radiators and an impedance matrix is used to obtain the acoustic surface pressure in terms of the shell radial velocity. To determine those regions of the cylinder responsible for the far field radiated sound, use is made of supersonic sound intensity (SSI). A method is proposed to calculate the SSI in the spatial domain for cylindrical shell structures which allows one to make direct use of the previously computed surface pressure and velocity distributions. The whole methodology is validated against finite element method (FEM) simulations and after that, results are presented for an acoustically thick shell. The roles played by the critical and ring frequencies are reported and the spectra of the acoustic power, radiation efficiency and far field acoustic pressure get analysed. It is shown that the annular ABH can become very effective when the cylinder flexural motion dominates over the circumferential one. The slow down of bending waves inside the ABH makes structural supersonic waves (in relation to sound speed) become subsonic at some point, which clearly diminishes the shell radiation efficiency. Overall, it is described why embedding an annular ABH on a cylindrical shell can strongly help reducing the radiated sound to the far-field.

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.

The characterization of the presence of bubbles in industrial fluid circuits may be extremely important for many safety issuses. It is well known that the acoustic properties of liquids can be drastically modified by a small amount of gaz content in the liquid. At sufficiently low frequencies, the speed of sound depends primarily on the gas volume fraction. The variation of the gas fraction may then induce some variations in the vibroacoustic behavior of the pipe transporting the liquid. Analysis of the pipe vibrations can then help in the monitoring of the bubble presence. In such a context, the aim of this study is to show how the the presence of bubbles in the liquid could affect the resonance frequencies of the pipe. A numerical vibroacoustical model has been developed to predict the vibroacoustical behavior of a stiffened cylindrical shell filled with a bubbly liquid exhibiting low frequency resonances. The model, experimentally verified with a well-characterized bubbly liquid, is then used to analyse the frequency shifts of the shell resonances in function of the bubble. Keywords : pipe, heavy fluid, numerical modelling, circumferential admittance approach, cylindrical shell, resonance frequency, void fraction

Substructuring methods are a very common and efficient way to solve complex vibroacoustic problems. The Condensed Transfer Function (CTF) approach is a substructuring method based on the concept of subsystem condensed transfer functions (corresponding to admittances or impedances) that allows assembling acoustical or mechanical subsystems coupled along lines or surfaces. For certain practical applications, it may be more efficient to subtract or to decouple a subsystem to a global system rather than assembling different subsystems. In this paper, a reverse formulation of the CTF method is proposed. This formulation allows us to predict the behavior of a subsystem that is part of a larger system, from the knowledge of the condensed transfer functions (CTFs) of the global system and of the residual subsystem that must be removed. For purposes of validation, the scattering problem of a rigid sphere in an infinite water domain impacted by an acoustic plane wave is considered. Comparisons with theoretical calculations are used to validate the formulation proposed and permit studying its accuracy for two types of condensation functions defining the CTFs.

A numerical technique is proposed for synthesizing realizations of airfoil surface pressure induced by incoming turbulence. In this approach, realization of the surface pressure field is expressed as a set of uncorrelated wall plane waves. The amplitude of these plane waves is determined from the power spectrum density function of the incoming upwash velocity fluctuation and the airfoil aeroacoustic transfer function. The auto-spectrum of the surface pressure is obtained from an ensemble average of different realizations. The numerical technique is computationally efficient as it rapidly converges using a relatively small number of realizations. The surface pressures for different airfoils excited by incoming turbulence are numerically predicted, and the results are compared with experimental data in the literature. Further, the unsteady force exerted on an airfoil due to the airfoil-turbulence interaction is also computed, and it is shown to be in very good agreement with analytical results.

Noise insulation in buildings is an important topic in building acoustics. Existing literature shows a clear lack of simulation tools for the design, analysis, and assessment of the sound insulation performance of building structures, especially when the frequency of interest becomes higher. To tackle this problem, a numerical based Condensed Transfer Function (CTF) method, alongside a piecewise calculation scheme, is adapted to investigate a simplified Double Skin Facade (DSF) system. Embracing a sub-structuring philosophy, the method offers an appealing alternative to existing analyses ones in terms of providing enhanced computational efficiency and enriched physical description of the system. Numerical analyses reveal dominant sound transmission paths into a typical receiving room. Meanwhile, as sound reduction devices, microperforated panels are investigated in two arrangements, triggering different sound absorption behaviors and design principles. The proposed model allows extensions to other building structures.

Cylindrical shells are often employed as simplified models to represent the physics of underwater vehicles. When a vehicle is moving underwater, the flow is likely to create a turbulent boundary layer (TBL) over the shell surface. The TBL induces vibrations on the shell, which results in the radiation of noise. Semi-analytical formulations are nowadays widely used to predict the vibro-acoustics of structures and re-design them to mitigate the flow-induced noise. However, most of the methods available in literature tackle the case of flat plates and only few results can be found for cylindrical shells. In this chapter, we give an overview of a method for calculating both the response of a fluid loaded cylindrical shell and the outward emitted noise, with different degrees of complexity. The considered test cases involve various phenomena and underlying physics. Aspects such as the role of propagative Bloch-Floquet waves in noise radiation by periodically stiffened structures, or the influence of mechanical coupling between the shell and non-axisymmetric inner structures are addressed. An explanation is also given for the very different behavior of the radiated acoustic pressure in the near and far fields.

A hybrid uncorrelated wall plane wave (UWPW) and finite element method (FEM) technique is introduced to the predict vibroacoustic response of a panel under turbulent boundary layer (TBL) excitation. The spectrum of the wall pressure fluctuations is evaluated from the TBL parameters and by using semi-empirical models from literature. TBL parameters can be estimated by different means, using theoretical formula, Reynolds-averaged Navier Stokes (RANS) simulations or experimental data. The wall pressure field (WPF) underneath the TBL is then synthesized by realisations of uncorrelated wall plane waves. The FEM is employed to compute the structural and acoustic responses of the panel for each realisation of uncorrelated wall plane waves. The responses are then obtained from an ensemble average of the different realisations. Selection criteria for cut-off wavenumber, mesh size and number of realisation are discussed. Two simply-supported baffled panels under TBL excitation are examined. Numerical results are compared with analytical results using the sensitivity functions of the panels, showing excellent agreement.

Substructuring methods are commonly used to solve vibroacoustic problems, as they allow studying complex systems by dividing them into smaller subsystems that can be studied separately. If they are generally used to couple subsystems, we are interested here in the decoupling procedure, consisting in subtracting a subsystem from a global system. Decoupling procedures can be used to perturbate an existing model in order to investigate the impact of a default on a given system, or to study problems with complex geometries, starting from a canonical system. In the framework of subtractive modelling, the reverse condensed transfer function (rCTF) method has been developed to decouple vibroacoustical subsystems that are initially coupled along lines or surfaces. The aim of this approach is to predict the response at any point of the final decoupled subsystem. The method will be presented on an academic test case consisting in the scattering problem of a plane wave by a rigid sphere immersed in an infinite water medium. Then, an example of industrial application will be proposed by studying the acoustic radiation of a partially coated cylindrical shell using the rCTF method.

International audience; The reproduction of the vibration and acoustic responses of structures under random excitation such as the diffuse acoustic field or the turbulent boundary layer is of particular interest to researchers and the transportation industry (automobile, aeronautics, etc.) as well. Indeed, the determination of these vibroacoustic responses requires making in-situ measurements or using test facilities such as the anechoic wind tunnel, which are complex and costly methods. Another drawback of these test means is the variability of the results when for instance; the same structure is tested in different facilities of the same kind. Based on the previous considerations, the necessity of finding a simple, cost-efficient and reproducible alternative method becomes obvious. In the present paper, a method of achieving this goal using a single acoustic source and the synthetic array principle is proposed. To assess the validity of this method, we propose an academic case study consisting of a baffled and simply supported aluminum panel under diffuse acoustic field and turbulent boundary layer excitations. The vibration response of the plate as well as the transmission loss are determined with the proposed process and compared to results from random vibration theory. These comparisons show good agreement between both the results obtained with the proposed approach and the theoretical ones.

International audience; Finding an alternative to common test means (reverberant chamber, wind tunnel facilities, in-situ measurements, etc.) is of particular interest to the transportation industry (automobile, aeronautics , etc.) for the reproduction of the vibroacoustic response of structures under random excitations such as the diffuse acoustic field or the turbulent boundary layer. In this paper a method of achieving this goal using a single acoustic source and the synthetic array principle is proposed. To assess the validity of this method, an academic case study consisting of a simply supported thin aluminum plate under turbulent boundary layer excitation is presented. The vibroacoustic response of the plate is determined with the proposed process and compared to results from random vibration theory and direct measurements in an anechoic wind tunnel facility. This comparison shows good agreement between the proposed approach and both the theoretical and wind tunnel results.

International audience; This work proposes a semi-analytical method to model the vibroacoustic behavior of submerged cylindrical shells periodically stiffened by axisymmetric frames and excited by a homogeneous and fully developed turbulent boundary layer (TBL). The process requires the computation of the TBL wall-pressure cross spectral density function and the sensitivity functions for stiffened cylindrical shells. The former is deduced from an existent TBL model and the latter are derived from a wavenumber-point reciprocity principle and a spectral formulation of the problem. The stiffeners' dynamic behavior is introduced in the formulation through circumferential admittances that are computed by a standard finite element code using shell elements. Four degrees of freedom are taken into account for the coupling between the shell and the stiffeners: three translation directions and one tangential rotation. To investigate the effect of the stiffeners on the radiated noise, two case studies are considered. The first one examines a fluid-loaded cylindrical shell with regularly spaced simple supports. The influence of Bloch-Floquet waves and the support spacing on the noise radiation are highlighted. The second case study inspects the fluid-loaded cylindrical shell with two different periodic ring stiffeners, namely stiffeners with T-shaped and I-shaped cross-sections. Their influence on the vibroacoustics of the shell is thoroughly analyzed.

A fully coupled structural–acoustic model of a cylindrical shell under external turbulent boundary layer excitation is herein developed. The numerical process requires computation of the wall pressure cross spectral density function as well as sensitivity functions for the fluid-loaded cylindrical shell. A semi-empirical model from literature is used to describe the wall pressure field induced by the turbulent boundary layer in the wavenumber–frequency domain. An analytical expression of the wall pressure field for a flat surface is adapted to describe the wall pressure field for a cylindrical surface. Circumferential sensitivity functions are derived using a wavenumber-point reciprocity principle. Results for the near-field and far-field acoustic pressure spectra are presented. Contributions of individual circumferential modes to the acoustic pressure spectra are examined, showing distinct trends below and above the ring frequency. The proposed method is computationally efficient and provides an effective approach to investigate vibroacoustic responses for maritime platforms.

© 2019 Elsevier Ltd In this work, a hybrid numerical approach to predict the vibrational responses of planar structures excited by a turbulent boundary layer is presented. The approach combines an uncorrelated wall plane wave technique with the finite element method. The wall pressure field induced by a turbulent boundary layer is obtained as a set of uncorrelated wall pressure plane waves. The amplitude of these plane waves are determined from the cross spectrum density function of the wall pressure field given either by empirical models from literature or from experimental data. The response of the planar structure subject to a turbulent boundary layer excitation is then obtained from an ensemble average of the different realizations. The numerical technique is computationally efficient as it rapidly converges using a small number of realizations. To demonstrate the method, the vibrational responses of two panels with simply supported or clamped boundary conditions and excited by a turbulent flow are considered. In the case study comprising a plate with simply supported boundary conditions, an analytical solution is employed for verification of the method. For both cases studies, numerical results from the hybrid approach are compared with experimental data measured in two different anechoic wind tunnels.

International audience; This paper proposes a numerically stable method for modelling a fluid-loaded multilayered cylindrical shell excited by a plane wave, which solves the fd instability problem that is usually observed when using the well-known transfer matrix method (TMM). In the considered modelling, each layer can be either a viscoelastic coating described by a general three-dimensional (3D) elasticity model or an intermediate perfect fluid layer. The transfer matrix of each layer relating the state vector at the layer's two interfaces is estimated with an appropriate standard method. Instead of multiplying together the layer transfer matrices in order to deduce the transfer matrix of the multilayer cylinder, we propose an alternative approach. This one consists in writing the continuity relations at each interface of the considered systems and in building a global matrix that can be solved to obtain the system response. As shown by numerical applications on typical naval test cases, the proposed global matrix assembly procedure as opposed to the classical TMM provides numerical stability over both a wide range of axial wavenumbers and circumferential orders, but also the ability to consider intermediate fluid layers. Besides, this model is well-suited to describe elastic solid layers of any anisotropy as illustrated by an additional case considering a transverse isotropic layer

Predicting the vibration response of an elastic structure excited by a turbulent flow is of interest for the civil and military transportation sector. The models proposed in the literature are generally based on the assumption that the turbulent boundary layer (noted TBL in the following) exciting the structure is spatially homogeneous. However, this assumption is not always fulfilled in practice, in particular when the excited area is close to the starting point of the TBL or with curved structures. To overcome this issue, this work proposes to extend two approaches generally used for dealing with homogeneous TBL, namely the spatial and the wavenumber approaches. The extension of the spatial approach to non-homogeneous excitation is relatively straightforward and gives us a reference, however with costly computation. On the contrary, extending the wavenumber approach requires more developments and assumptions that have led the authors to develop a sub-area decomposition technique (SDT). It consists in partitioning the excited area in several sub-areas, assuming a homogeneous TBL pressure field on each sub-area and neglecting certain interactions between the sub-areas. A criterion on the sub-area size as a function of the minimum wavelength of the wall pressure field is proposed on the basis of the numerical calculations. A test case on a plate with varying thickness and excited by a growing TBL allows us to highlight: (1) the interest of the SDT compared to a classical calculation considering a homogeneous TBL; (2) the efficiency of the SDT in terms of computing time compared to the spatial approach.

International audience; The understanding of the influence of non-axisymmetric internal frames on the vibroacoustic behavior of a stiffened cylindrical shell is of high interest for the naval or aeronautic industries. Several numerical studies have shown that the non-axisymmetric internal frame can increase the radiation efficiency significantly in the case of a mechanical point force. However, less attention has been paid to the experimental verification of this statement. That is why this paper proposes to compare the radiation efficiency estimated experimentally for a stiffened cylindrical shell with and without internal frames. The experimental process is based on scanning laser vibrometer measurements of the vibrations on the surface of the shell. A transform of the vibratory field in the wavenumber domain is then performed. It allows estimating the far-field radiated pressure with the stationary phase theorem. An increase of the radiation efficiency is observed in the low frequencies. Analysis of the velocity field in the physical and wavenumber spaces allows highlighting the coupling of the circumferential orders at the origin of the increase in the radiation efficiency.

Proceedings of the ICA 2019 and EAA Euroregio : 23rd International Congress on Acoustics, integrating 4th EAA Euroregio 2019 : 9-13 September 2019, Aachen, Germany / proceedings editor: Martin Ochmann, Michael Vorländer, Janina Fels 23rd International Congress on Acoustics, integrating 4th EAA Euroregio 2019, ICA 2019, Aachen, Germany, 9 Sep 2019 - 13 Sep 2019; Aachen (2019)., Published by Aachen

International audience; Whereas the coupling between modes of two different subsystems is well-resolved in vibroacoustic energy-based methods, the situation becomes more intricate when several subsystems get connected at a common junction. In statistical energy analysis (SEA), the modal formulation is replaced by the travelling wave approach to solve the problem. However, this is not a viable option for other energy-based methods, like the statistical modal energy distribution analysis (SmEdA), and a modal coupling scheme is required for them. If there is a strong impedance mismatch between the multiple connected subsystems, the displacement-stress dual formulation offers a proper way to address the situation. Yet, the latter fails if all involved subsystems have similar stiffness. In this work, the feasibility of the Craig-Bampton (CB) method to address such circumstance is explored. It is shown that the original CB technique does not fulfill the modal coupling assumptions of energy-based methods, so it is suggested to reformulate it to partially mitigate the problem. Numerical tests on a benchmark problem are carried out to validate the proposal. The benchmark consists of a floor coupled with two walls at right angle, and it is analyzed for different impedance mismatch conditions.

International audience; Statistical energy methods in vibroacoustics, like the statistical energy analysis (SEA) or the statistical modal energy distribution analysis (SmEdA), rely on specific modal coupling assumptions (MCAs) between subsystem modes. These methods assume that the behavior of subsystem mode amplitudes mimic that of oscillators, that the modes within a subsystem are uncoupled, and that the coupling between two different subsystems only takes place through the interaction of resonant modes. In the case of more than two subsystems being connected at a junction, however, it becomes difficult to establish a modal interaction scheme for them. In SEA, the problem is avoided by resorting to the travelling wave approach instead of the modal one. Nevertheless, there is a need for other energy-based methods, like SmEdA, to deal with such a situation. In this work it is proposed to extend the displacement-stress dual formulation, originally intended for two subsystems, to the case of multiple flexural waveguides connected at a junction. Numerical results are presented for a test case consisting of a floor coupled to two walls at right angle. The fulfillment of the MCAs by the dual modal formulation is examined in terms of the impedance mismatch between the floor and the walls.

International audience; Current designs of acoustic black holes are mainly intended for straight beams and flat plates. However, many structures of interest in naval and aeronautical applications essentially consist in a periodically stiffened cylindrical shell, which could benefit from the acoustic black hole (ABH) effect to reduce vibrations and noise radiation. In this work, we suggest the design of annular ABHs to that purpose. To test the feasibility of such annular ABHs we consider the idealized case of a periodically simply supported cylindrical shell of infinite length. Such a structure allows for the propagation of Bloch-Floquet flexural waves at some passbands, which can play an important role in the radiation of noise at the far field. By means of wave finite element models, we show that the proposed annular ABHs constitute an effective way of reducing the shell flexural motion.

International audience; Acoustic stealth is one of the main operational capabilities for a submarine vehicle. To meet always stricter requirements in terms of radiated noise, it is important for the shipbuilder to be able to predict the noise at the early design stages. One of the key elements is the transfer function between a mechanical excitation on the pressure hull of the submarine vehicle and the far-field pressure radiated into water. This transfer function is commonly called p/F. A dedicated numerical method, called the Condensed Transfer Function (CTF) method, has been developed to calculate the vibro-acoustic behavior of a submarine hull. The method is based on a substructuring approach, where a model of an infinite fluid-loaded cylindrical shell is coupled to models of internal structures such as stiffeners and bulkheads. The fluid-loaded cylindrical shell is described analytically, while the internal structures are modeled by the finite element method (FEM). For each uncoupled subsystem, mechanical admittances are calculated at the junctions between the subsystems, and approximated with a set of functions called condensation functions. The interactions between the subsystems are estimated using the superposition principle, the force equilibrium and the displacements continuity. Compared to fully analytical models, the CTF method has more flexibility on the geometry of the internal frames. Compared to models completely described by the FEM, the present approach has lower calculation cost. Consequently, transfer functions can be calculated on a wide frequency range (from some Hz to several kHz) with limited calculation costs. Besides, an experimental campaign has been conducted to measure the transfer function p/F of a scaled model of the pressure hull. Based on laser vibrometer measurements on a model in air, the radial acceleration are measured at the surface of the shell. The far-field radiated pressure is calculated through the stationary phase theorem to deduce the transfer function p/F. This approach has two main advantages. First, no microphones are needed to estimate the radiated noise from the shell and second, the directivity of the radiated pressure can be studied. In this paper, the principle of both the numerical and the experimental approaches are described. A test case is presented and the results using both approaches are compared. The directivity pattern and some physical features of the vibro-acoustic behavior of the hull are discussed.

International audience; The numerical simulation of beams and plates with embedded acoustic black holes (ABHs) is computationally demanding because of the very thin thickness attained at the ABH central area. Semi-analytical approaches relying on the Rayleigh-Ritz method with wavelet or Gaussian basis functions have thus revealed as an accurate and fast alternative to determine the ABH vibration field in parametric studies. To date however, the vast majority of works on ABHs have only dealt with ABH indentations on straight beams and flat plates. It would be also worth exploring the feasibility of ABHs to control the vibrations of curved shells, typically found in aerospace and naval structures. In this work, we address this issue and extend the Gaussian expansion method (GEM) to characterize annular ABHs embedded on cylindrical shells. First, we show how the GEM can be modified to make Gaussian shape functions satisfy periodic boundary conditions in the circumferential direction of the cylinder. The GEM is then used to determine the vibration field of the ABH cylindrical shell and gets validated by comparison with finite element simulations. A thorough analysis of the performance of the annular ABH follows, which stresses the differences with the behavior of ABHs on flat surfaces. In particular, we show the influence that waves propagating in the circumferential direction have on the operational frequency range of the ABH. The effects of the viscoelastic layer and the inclusion of longitudinal stiffeners to strengthen the cylinder rigidity are also analyzed by means of the proposed GEM approach. This work broadens previous semi-analytical methods to start investigating the ABH effect on curved structures.

International audience; Whereas the spatial coherence of wall pressure and vibratory fields induced by turbulent boundary layers (TBLs) on flat plates have been studied at extent, their equivalents for cylindrical structures still need further investigation. To that end, this work develops a semianalytical model which is valid for infinite cylindrical shells filled with a heavy fluid and excited by an internal TBL. The cylindrical shell can be also coupled to two ring stiffeners that account for the flanges generally used to connect a pipe to other portions of a circuit. The crossspectrum density (CSD) function of the shell radial accelerations is estimated from the system circumferential sensitivity functions and the CSD of the wall pressure field induced by the TBL. The spatial coherence of the pipe vibration field is therefore analysed for a pipe with and without flanges. This is of critical importance for applications such as non-intrusive techniques for detecting acoustic sources inside pipes, like beamforming using arrays of accelerometers. If the pipe conveys a flow, the beamforming efficiency can strongly deteriorate because of the background noise induced by the TBL, which pollutes the coherence signal between sensors. The effects that the spatial coherence could have on the beamforming results of a line of point sensors (accelerometers) and a ring of wire sensors (piezoelectric coiled wires) are also investigated in this paper.

International audience; The scattered pressure from a stiffened axisymmetric submerged shell impinged by acoustic plane waves has been investigated experimentally, analytically and through numerical models. In the case where the shell is periodically stiffened, it is shown that helical, Bragg, and Bloch-Floquet waves can propagate. The influence of non-axisymmetric internal frames on these scattering phenomena is nevertheless not well known, as it can considerably increase the computational cost. To overcome this issue, the Condensed Transfer Function method, which has been developed to couple subsystems along linear junctions in the case of a mechanical excitation, is extended to acoustical excitations. It consists in approximating transfer functions on the junctions and deducing the behavior of the coupled system using the superposition principle and the continuity equations at the junctions. In particular, the CTF method can be used to couple a dedicated model of an axisymmetric stiffened submerged shell with non-axisymmetric internal structures modeled by the Finite Element Method. Incident plane waves are introduced in the formulation and far-field reradiated pressure is estimated. An application consisting of a stiffened shell with curved plates connecting the ribs is considered. Supplementary Bloch-Floquet trajectories are observed in the frequency-angle spectrum and are explained using a simplified interference model.

International audience; In recent years, acoustic black holes (ABHs) have revealed as a very effective method for the passive reduction of vibrations in flat plates and straight beams. Those essentially consist of circular indentations and/or side boundaries, whose thicknesses decrease to zero following a power-law profile. Nonetheless, many structures in the aeronautical and naval sectors, among others, involve cylindrical structures with periodic stiffeners or supports. Such periodic structures admit the propagation of Bloch-Floquet (BF) bending waves at some frequency passbands, which may result in strong vibration levels and noise radiation. In this work, we propose the design of annular ABHs to mitigate the problem. A wave finite element model is first used to determine the frequency passbands on an ideal, periodically simply supported cylindrical shell of infinite length, with embedded annular ABHs. Then, a long, but now finite simply supported cylindrical shell, is presented to show how the transmissibility between two sections strongly diminishes with the inclusion of ABHs. That confirms annular ABHs as a very effective means of reducing BF wave propagation. Unfortunately, embedding ABHs on the shell weakens its structural rigidity so a thorough analysis is made on the effects of inserting stiffeners in the longitudinal direction to partially remedy that inconvenient. Quite surprisingly, it is shown that the inclusion of stiffeners can even enhance the performance of the ABHs for some configurations. To finally foresee the potential of annular ABHs for practical applications, a finite element simulation is made on a slightly more realistic geometry, resembling a very simplified version of the hull of a submarine vehicle or a gas tank.