A fundamental study on the sound radiation from ribbed vibrating panels.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

Synthesis of wall pressure fields of non-homogeneous turbulent boundary layers for vibroacoustic simulations.

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.

Acoustic radiation from a cylindrical shell with a voided soft elastic coating.

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.

A spectral global matrix method for modelling the response of a fluid-loaded multilayered cylindrical shell excited by an acoustic plane wave.

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.

Experimental prediction of the vibration response of panels under a turbulent boundary layer excitation from sensitivity functions.

This study aims at validating an experimental method for characterizing the vibration behavior of panels excited by a turbulent boundary layer (TBL) excitation as a possible alternative to standard means like wind tunnels or in situ tests. The approach takes advantage of an explicit separation of the excitation contribution from the dynamic behavior of the panel. Based on the measurement of deterministic transfer functions on the panel, called "sensitivity functions," which are then combined with either measurements or a model of the wall-pressure fluctuations induced by the TBL excitation, the vibration response under such an excitation can be retrieved. For validation purposes, the wall-pressure fluctuations of the turbulent flow generated in an anechoic wind tunnel are measured with a flush-mounted microphone array. The decay rates and the convection velocity, which mainly characterize the excitation, are extracted from these measurements. The plate velocity response to this excitation is estimated following the proposed method using the measured sensitivity functions and the model of Mellen fed with experimentally estimated decay rates and convection velocity. A comparison between a directly measured vibration auto-spectrum under the actual flow and the one predicted following the suggested method shows satisfactory agreement.

Convergence criteria on the acoustic velocity continuity in a panel-cavity system.

Modal-based acoustoelastic formulation is regarded as the cornerstone of vibro-acoustics and has been widely used for coupling analyses of structure-cavity systems. The controversy and the skepticism surrounding the acoustic velocity continuity with the surrounding vibrating structures have been persistent, calling for a systematic investigation and clarification. This fundamental issue of significant relevance is addressed in this paper. Through numerical analyses and comparisons with wave-based exact solution, an oscillating convergence pattern of the calculated acoustic velocity is revealed. Normalization of the results leads to a unified series truncation criterion allowing minimal prediction error, which is verified in three-dimensional cases. The paper establishes the fact that the modal based decomposition method definitely allows correct prediction of both the acoustic pressure and the velocity inside an acoustic cavity covered by a flexural structure upon using appropriate series truncation criteria.

Vibroacoustic response of panels under diffuse acoustic field excitation from sensitivity functions and reciprocity principles.

This paper aims at developing an experimental method to characterize the vibroacoustic response of a panel to a diffuse acoustic field (DAF) excitation with a different laboratory setup than those used in standards (i.e., coupled rooms). The proposed methodology is based on a theoretical model of the DAF and on the measurement of the panel's sensitivity functions, which characterize its vibroacoustic response to wall plane waves. These functions can be estimated experimentally using variations of the reciprocity principle, which are described in the present paper. These principles can either be applied for characterizing the structural response by exciting the panel with a normal force at the point of interest or for characterizing the acoustic response (radiated pressure, acoustic intensity) by exciting the panel with a monopole and a dipole source. For both applications, the validity of the proposed approach is numerically and experimentally verified on a test case composed of a baffled simply supported plate. An implementation for estimating the sound transmission loss of the plate is finally proposed. The results are discussed and compared with measurements performed in a coupled anechoic-reverberant room facility following standards.

Simulation of the pressure field beneath a turbulent boundary layer using realizations of uncorrelated wall plane waves.

This paper investigates the modeling of a vibrating structure excited by a turbulent boundary layer (TBL). Although the wall pressure field (WPF) of the TBL constitutes a random excitation, the element-based methods generally used for describing complex mechanical structures consider deterministic loads. The response of such structures to a random excitation like TBL is generally deduced from calculations of numerous Frequency Response Functions. Consequently, the process is computationally expansive. To tackle this issue, an efficient process is proposed for generating realizations of the WPF corresponding to the TBL. This process is based on a formulation of the problem in the wavenumber space and the interpretation of the WPF as uncorrelated wall plane waves. Once the WPF has been synthesized, the local vibroacoustic responses are calculated for the different realizations and averaged together in the last step. A numerical application of this process to a plate located beneath a TBL is used to verify its efficiency and ability to reproduce the partial space correlation of the excitation. To further illustrate the proposed method, a stiffened panel modeled using the finite element method is finally examined.

A substructuring approach for modeling the acoustic scattering from stiffened submerged shells coupled to non-axisymmetric internal structures.

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 (CTF) 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.

Prediction of flow induced sound and vibration of periodically stiffened plates.

Stiffened structures excited by the turbulent boundary layer (TBL) occur very frequently in engineering applications; for instance, in the wings of airplanes or the pressure hulls of submarines. To improve knowledge of the interaction between stiffened structures and TBL, this paper deals with the modeling of infinite periodically stiffened plates excited by TBL. The mathematical formulation of the problem is well-established in the literature. The originality of the present work relies on the use of a wavenumber-point reciprocity technique for evaluating the response of the plate to convected harmonic pressure waves. It follows a methodology for estimating the vibro-acoustic response of the plate excited by the TBL from the wall pressure spectrum and its displacements in the wavenumber space due to point excitations located at the receiving positions. The computing process can be reduced to the numerical integration of an analytical expression in the case of a periodically stiffened plate. An application to a naval test case highlights the effect of Bloch-Floquet waves on the vibrations of the plate and its radiated pressure in the fluid.

Prediction of the vibro-acoustic behavior of a submerged shell non periodically stiffened by internal frames.

This paper describes the development of a numerical model to predict the vibro-acoustic behavior of an externally fluid loaded shell with non-uniformly space stiffeners and transversal bulkheads. This model constitutes an extension of the existing semi-analytic capability in predicting the acoustics of axisymmetric structures. It is based on the circumferential admittance approach (CAA) which consists in substructuring the problem so that the fluid loaded shell constitutes one subsystem and the frames constitute other independent subsystems. These subsystems are coupled together by assembling the circumferential admittances that characterize each uncoupled subsystem. Different numerical approaches can be used to estimate these admittances. The standard finite element code is well adapted for evaluating the admittances of the internal frames whatever their cross-section geometries and material properties. Classical discretization methods such as finite elements and boundary elements are too time-consuming for the fluid loaded shell. To avoid this obstacle, three different approaches with different degrees of approximation are proposed to estimate the shell admittances. Comparisons with a reference case are proposed to evaluate the accuracy and the efficiency of each of these three approaches. With the optimal approach, CAA gives very good results in satisfactory computing time. It is well-adapted for analyzing the behavior of a submarine pressure hull in a wide frequency range of interest.