Diffuse Acoustic Field Research Articles

Experimental synthesis of random pressure fields based on Transfer-Matrix analysis on 1D arrays

Synthesizing random pressure fields with loudspeaker arrays in a laboratory setting requires acquiring a global transfer matrix of all channels between the loudspeaker array and the microphone array. This inevitably involves measuring a large and unwieldy number of transfer functions. Therefore, we propose a prediction method for the transfer matrix under free-field conditions, combining a substantially reduced number of measurements with specific predictions based on segmented acoustic centers. In free-field conditions, if only three sets of transfer functions are measured for each loudspeaker and the remaining entries in the global transfer matrix are predicted using analytical expressions, the results show that the normalized error between the predicted and measured transfer matrices can be less than -13 dB. The experimental results indicate that, based on a one-dimensional loudspeaker array in a standard anechoic chamber, this prediction method shows promise for accurately reproducing random pressure fields, such as a diffuse acoustic field and the pressure field in the spanwise direction of a turbulent boundary layer. Additionally, the prediction method demonstrates the potential for extension to two-dimensional synthesis.

Computation of the sound transmission loss of heterogeneous periodic structure using the wave finite element-based methodology

In the present study, a Wave Finite Element-based method is introduced to estimate the Sound Transmission Loss (STL) of periodic structures with contrasting properties. This method addresses the precision and computational speed limitations of existing methodologies. It calculates the wave STL by applying a plane wave excitation from the ambient medium to a Unit Cell (UC), which is representative of the periodic structure. The STL under Diffuse Acoustic Field (DAF) is then computed by integrating the wave STL over all possible incidence angle ranges. The advantages of this methodology are demonstrated through various configurations, ranging from simple plates to complex laminated structures. Additionally, the study investigates the Mass Law of STL.

Estimating direction of arrival in reverberant environments for wake-word detection using a single structural vibration sensora).

The vibrational response of an elastic panel to incident acoustic waves is determined by the direction-of-arrival (DOA) of the waves relative to the spatial structure of the panel's bending modes. By monitoring the relative modal excitations of a panel immersed in a sound field, the DOA of the source may be inferred. In reverberant environments, early acoustic reflections and the late diffuse acoustic field may obscure the DOA of incoming sound waves. Panel microphones may be especially susceptible to the effects of reverberation due to their large surface areas and long-decaying impulse responses. An investigation into the effect of reverberation on the accuracy of DOA estimation with panel microphones was made by recording wake-word utterances in eight spaces with reverberation times (RT60s) ranging from 0.27 to 3.00 s. The responses were used to train neural networks to estimate the DOA. Within ±5°, DOA estimation reliability was measured at 95.00% in the least reverberant space, decreasing to 78.33% in the most reverberant space, suggesting an inverse relationship between RT60 and DOA accuracy. Experimental results suggest that a system for estimating DOA with panel microphones can generalize to new acoustic environments by cross-training the system with data from multiple spaces with different RT60s.

A semi-analytical method using auxiliary sine series for vibration and sound radiation of a rectangular plate with elastic edges

This paper proposes an efficient semi-analytical method using auxiliary sine series for transverse vibration and sound radiation of a thin rectangular plate with edges elastically restrained against translation and rotation. The formulation, constructed by two-dimensional sine and/or cosine series, can approximately express the bending displacement, and calculate vibration and sound radiation under excitation of point force, arbitrary-angle plane wave, or diffuse acoustic field with acceptable accuracy. It is also applied for baffled or unbaffled conditions. A post-process program is developed to predict vibrating frequencies and modes, mean square velocity spectrum, and sound transmission loss via reduced-order integrals of radiation impedances. The method is validated by experiment and simulation results, demonstrating accurate and efficient computation using a single program for transverse vibration and sound radiation of a plate under different elastic boundary conditions and different excitations. Formulas given in this paper provide a basis for the code development on transverse vibration and sound radiation analysis of thin plates.

Nonlinear vibrations of a ballistic vehicle with friction joints subjected to vibroacoustic excitation - experiments, modeling and simulations

This study presents the experiments, modeling and numerical simulations of an industrial aeronautical structure subjected to vibroacoustic excitation. In flight, especially during atmospheric re-entry, an aeronautical structure is exposed to major pressure fluctuations on its external surface. These fluctuations are described as a dynamic excitation which generates structural vibrations of the outer surface and of the components inside the aeronautical structure. Due to some of these internal components such as joints, the assembly may exhibit a nonlinear vibration response. The simulation of these nonlinear vibrations requires reliable modeling of the wall pressure fluctuations and a nonlinear vibration simulation method adapted to the nonlinear modeling of the structure. In this study, a modeling and simulation method is developed to compute the nonlinear vibration response of an industrial assembly to such a surface, random, correlated dynamic excitation. More specifically, numerical simulations are performed by proposing an extension of the well-known Harmonic Balance Method for nonlinear mechanical systems subjected to complex vibroacoustic excitation. The method is validated using a dedicated ground experiment. A metallic industrial assembly representing a ballistic vehicle and including friction joints is used. This structure is subjected to controlled vibroacoustic excitation: diffuse acoustic loading in a reverberant chamber. The structure exhibits a nonlinear vibration response due to friction. The finite element model is validated through an experimental modal analysis with an electrodynamic shaker. The vibroacoustic modeling of the excitation is then validated through a test-simulation comparison using diffuse acoustic field testing at low excitation level. Then the global nonlinear simulation process is validated using diffuse acoustic field testing at increasing excitation levels. Test and simulation results exhibit the same nonlinear behavior: increase of dissipation and softening effect at the main resonances. This work thus represents a new step towards the use of nonlinear vibration simulation methods with real industrial structures and real-life loading.

Extension of the source scanning technique to curved rectangular panels for the vibroacoustic characterization of structures using wall-pressure plane waves

The Source Scanning Technique (SST) is an experimental method used to synthesize the vibroacoustic response of a given structure under random excitations such as the Diffuse Acoustic Field (DAF) and the Turbulent Boundary Layer (TBL) using a single monopole source. It was previously developed and validated for simple plane structures such as Flat Rectangular Panels (FRPs). However, in industrial cases, the structures of interest can be more complex. In this paper, the feasibility of the extension of SST to Curved Rectangular Panels (CRPs) is investigated. To numerically evaluate the performances of SST when generating wall-pressure plane waves (WPPWs) on CRPs, analytical developments are proposed to estimate the transfer functions between the monopole source and the CRPs. Two- and three-dimensional cases are considered and validated using the boundary element method. Then, parametric studies are carried out to determine the optimal parameters for implementing the SST process in two- and three-dimensional cases considering a conformal geometry, i.e., the array of monopoles has the same geometry as the structure of interest. The numerical results obtained are then supported by experimental investigations using a robotized system to move the monopole source. The transfer functions obtained using the proposed analytical models are compared to the measured ones, yielding relatively good agreement between the results.

Estimation of acoustical materials sound absorption coefficient under oblique incidence plane wave and diffuse field via Allard model inversion

A technique for estimating the sound absorption of materials under oblique incidence plane wave and diffuse field excitations is proposed. It requires a mobile loudspeaker and a pair of fixed microphones above a layer of absorbing material. Starting from sound pressure measurements made above the material surface for multiple source positions and by inverting Allard’s propagation model, the proposed method allows for the identification of two effective (or equivalent) parameters, namely, the complex effective density and the complex wave number. Obtaining these parameters makes it possible to estimate the sound absorption coefficient for a plane wave with any angle of incidence or under a diffuse acoustic field by summation over the angles. The results are compared to theoretical values calculated using the Johnson-Champoux-Allard model and to reference measurements obtained using an impedance tube, a small cabin, a large reverberant room, and a sound field synthesis method. One of the limitations of this method lies in the assumptions associated with the Allard model to describe the sound field above the material (assumed to be isotropic, homogeneous, of constant thickness, and to behave like an equivalent fluid). The main advantages are (1) that the sound absorption coefficient can be estimated under oblique incidence plane wave and diffuse acoustic field with values that are always in a physical range (between 0 and 1), and (2) that samples of the order of the square meter without specific preparation can be tested which reduces the constraints associated with impedance tube or reverberant room measurements.

Non-destructive reverberant testing of natural fibrous samples in a diffused acoustic field environment

A hexahedron reverberation box was utilized to measure the reverberation time of samples in a diffuse acoustic field. The aim of this study is to design a mathematical model that accurately represents the correlation between frequency and absorption coefficient for analysis. The same was obtained by aligning the noise absorption coefficients (NACs) determined through an impedance tube and calculated based on the reverberation time. The analysis indicated that jute fiber exhibits superior performance compared to other natural fibers, such as rock and glass wool, in the attenuation of sound frequencies above 2200 Hz. The results motivated further investigation over jute nonwoven fabric to conduct layer analysis (1–7) and to examine the impact of thickness. Thereby, a dataset was compiled consisting of 11 fibrous samples (nine natural and two commercial fibers) and jute nonwoven fabric. The empirical model was developed regardless of the type of fiber or thickness of the nonwoven fabric, and it was successfully validated for three additional fibers (banana, pineapple, and ramie). The predictive model exhibited a high level of accuracy in estimating the NAC, displaying a strong similarity to that of impedance tube measurements. The achieved mean absolute error ranges for the predictions are between 0.02 and 0.03 only. The main discovery of this study revolves around the recognition of frequency of sound as a crucial variable and its application in predicting the NAC for the samples.

Use of metamaterials to reduce underwater noise generated by ship machinery

Reducing underwater noise pollution from ship machinery is a significant challenge. Ship machinery usually operates at fixed speeds and emits tonal noise with large amplitudes at low frequencies. Conventional soundproofing materials are inadequate for absorbing tonal noise and require large thicknesses at low frequencies. Quarter-wavelength resonators effectively absorb sound at their fundamental frequency and odd harmonics. Still, the applicability of this solution is nevertheless limited by its length requirement, which becomes cumbersome at low frequencies and, thus, large wavelengths. This study explores different structured metamaterial designs based on labyrinth, coiled quarter-wavelength resonators, and hybrid configurations combining glass wool and coiled resonators. Analytical, numerical calculations, and experimental tests are carried out under normal plane wave incidence (using an impedance tube) and a diffuse acoustic field (in a small reverberant cabin). In particular, a numerical optimization based on a periodic unit cell model is used to optimize the hybrid configuration and analyze its behavior under variable plane wave incidence angles. Preliminary tests conducted in a water basin using a small, straightforward aluminum box equipped with some proposed designs indicate reductions in underwater noise levels. The proposed solutions offer limited-cost and compact solutions for mitigating machinery noise and, potentially, the preservation of marine ecosystems.

Active design of diffuse acoustic fields in enclosures.

This paper presents a numerical framework for designing diffuse fields in rooms of any shape and size, driven at arbitrary frequencies. That is, we aim at overcoming the Schroeder frequency limit for generating diffuse fields in an enclosed space. We formulate the problem as a Tikhonov regularized inverse problem and propose a low-rank approximation of the spatial correlation that results in significant computational gains. Our approximation is applicable to arbitrary sets of target points and allows us to produce an optimal design at a computational cost that grows only linearly with the (potentially large) number of target points. We demonstrate the feasibility of our approach through numerical examples where we approximate diffuse fields at frequencies well below the Schroeder limit.

Coiled quarter wavelength resonators for low-frequency sound absorption under plane wave and diffuse acoustic field excitations

To reduce their space requirement, quarter wavelength resonators are coiled up into a spiral to have the shape of a flat cylinder. The practical implementation of these resonators is tested using 3D printing, laser cutting and machining. Numerical simulations and impedance tube measurements are first compared for a normally incident plane wave excitation. This step allows to evaluate the effect of the resonator’s inlet diameter, internal wall thickness, overall height as well as its constitutive material. A series of samples are then 3D printed following the identified optimal geometrical configuration. An array of resonators is tested alone and in combination with a glass wool layer under diffuse acoustic field excitation in a small reverberation chamber. The obtained results show that coiled quarter wavelength resonators can provide large sound absorption at their lowest resonance frequency and under both considered excitations, even if the largest external dimension of the resonators is only 1/18th of the targeted acoustic wavelength.

Excitation of structures by partially correlated pressures: A review of diffuse acoustic field and turbulent boundary layer models

Structures are sometimes excited by pressure distributions which exhibit complex spatial correlation. This differs from common acoustic excitations since the pressure at one location is only partially correlated with the pressure at another location due to inherent spatial randomness within the forcing function. Two forcing functions which exhibit partially-correlated pressures are the diffuse acoustic field (DAF) and turbulent boundary layer (TBL) flow. A basic model for representing the spatial correlation for these two forcing functions will be reviewed in both the spatial and wavenumber domains. Recent approaches for computing the vibration of structures excited by DAF or TBL flow will then be summarized. Interesting physical effects, such as intermodal coupling, will be highlighted to illustrate the importance of properly modeling partial correlations when they exist.

On the vibro-acoustic modeling of panels excited by diffuse acoustic field (DAF)

Composite materials along with isotropic materials possess abundant applications to various engineering disciplines like aerospace and mechanical issues. The design optimization of composite materials such as sandwich panels essentially needs an accurate vibro-acoustic modeling. Such a modeling of these materials and a sound synthesis can lead to a design approach based on relevant psychoacoustic analyses. In this research, the mathematical/numerical and experimental steps required by the vibro-acoustic modeling of composite and isotropic plates excited by a diffuse acoustic field (DAF) are discussed. Herein, the analytical modeling was performed by 4th and 6th order problems adapted for the composite and isotropic plates, and moreover, the numerical modeling was carried out via the Finite Element Method (FEM). The experimental observations were also performed by means of an acoustic test cabin used for ideally generating a diffuse acoustic field (DAF). The various types of analytical and numerical simulations including synthesized sounds required by future psycho-acoustic analyses, as well as experimental observations including recorded sounds were investigated and compared. Finally, based on the various analyses, the research illustrates how such investigations and comparisons are necessary for designing and enhancing the mechanical and vibro-acoustic properties of materials.

A Review on Vibro-Acoustic Analysis of a Launch Vehicle Structure

Abstract: Space vehicles are subjected to significant dynamic pressure loads when their rocket propulsion systems are in use during flying missions. During the aerodynamic and launch phases, launch vehicles, payloads, and their parts are subjected to extremely high random acoustic loads. The noise from the engine exhaust gas, aerodynamic boundary layer noise, transonic buffering, structure-borne vibration, engine thrust fluctuation, etc. is the source of these loads, which also result in a secondary acoustic load. When the vehicle is lifting off and traveling at a speed greater than Mach number, acoustic stresses to the spacecraft and payload are very harsh and significant. This loading causes the structure to vibrate randomly, which could be dangerous for some vehicle parts, avionics, propulsion systems, and payloads like satellites. This paper discusses the vibration of the structure subjected to acoustic excitation on a diffuse acoustic field and the software used for the analysis.

Vibro-Acoustic Modelling of Aeronautical Panels Reinforced by Unconventional Stiffeners

The purpose of this work is to characterise the vibro-acoustic behaviour of rectangular flat panels reinforced by “unconventional” stiffeners. Such panels are being increasingly employed in the aircraft industry in the case of composite fuselage, so that the assessment of the most efficient and accurate numerical techniques and modelling procedures to correctly predict their dynamic and acoustic behaviour is required. To this end, an analytical method, available from literature, has been initially employed to investigate on the main attributes of sound transmission loss properties of stiffened panels driven by an acoustic diffuse field excitation. Based on existing commercial codes, different numerical techniques have been implemented and deeply examined to assess their potentiality and restrictions. Among them, the Hybrid method has been eventually identified as the best compromise in terms of accuracy and computational effort. The drawbacks of deterministic and even Hybrid numerical approaches for medium–high frequency vibro-acoustic analysis when dealing with large structures, make use of the pure SEA approach compulsory. In particular, a refined tuning of a specific feature made available within the employed SEA analysis environment when dealing with reinforced shells is implemented as a potential solution to overcome the complexity in correctly modelling the examined unconventionally stiffened panels.

Measurement and Characterisation of a Diffuse Acoustic Field Using a Phased Array

A diffuse acoustic field has been increasingly used to infer temporal changes in the structures, such as early dislocations and microcracking. This study explores three different techniques to characterise acoustic field by using a single ultrasonic phased array. The first two techniques are proposed to measure spatial uniformity of wave field by examining differences in the integral of energy and the maximum energy respectively at multiple inspection locations. The third one is developed to evaluate the degree of phase coherence between propagating waves transmitted sequentially by two neighbouring array elements. The efficacy of these techniques are investigated by examining their metrics on simulations and well-known samples. The results suggest that two selected metrics can be used to quantitatively estimate the diffuse field start time as well as the field size by comparing their value with the idealised diffuse state (15% for the energy integral metric, ηarea and 1 for the phase coherence metric, ηphase) and identifying the convergence start point.

Impact of a tunnel on the TL of a vehicle floor in bare and trimmed conditions and investigation on the most suitable simplified geometry able to better represent such impact

NVH engineers are faced with the challenge of designing trim parts for vehicle interior and exterior, like inner dash insulators, carpets, underbody shields or engine encapsulations, which can be made with very different Bills of Materials (BOMs) including among others foams, felts or heavier layers. The measurables commonly used to rank various solutions are Transmission Loss (TL) and absorption. Depending on the numerical analysis method, different approaches may be considered for the evaluation of the TL of an automotive component. In particular, in Statistical Energy Analysis (SEA), automotive components are modeled as an assembly of panels having a simple shape, e.g. flat panels and/or panels with single or double curvature. Furthermore, in SEA the trim is normally modeled by means of the Transfer Matrix Method (TMM), which is essentially a 2-dimensional methodology. This paper intends to analyze in some depth the level of approximation that these practices bring with themselves, specifically in relation to the modelling of an automotive floor. More in detail, the aim of the paper is first to investigate what impact has the presence of the tunnel on the TL of a vehicle floor in bare and trimmed conditions and then to evaluate if the presence of the tunnel can be better modeled by using a semi-cylinder or three flat plates welded together in a trapezoidal shape, both shapes considered as a reasonable simplification of the actual geometry of a typical tunnel. The analysis is carried out at simulation level using FE. To investigate both air bone noise and structure borne noise transmission, two types of excitations are used: a diffuse acoustic pressure field applied to the entire floor surface and an imposed displacement applied to the edge of the floor surface. Furthermore, 3 different kind of trims are taken into consideration in order to analyze if and how the tunnel modeling strategy may influence the evaluation of the trim effectiveness.

Reproduction of the vibroacoustic response of panels under stochastic excitations using the source scanning technique

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.

Assessment of statistical features of the diffused acoustic field in a test section of a cavitation tunnel

Noise measurements in a cavitation tunnel is the preferred approach for predicting the underwater noise radiated by a propeller at sea. The accuracy of the prediction is linked to the similitude laws used to transform the model scale measurements to the full-scale ones. Besides, this accuracy is obviously linked to the accuracy of the model scale measurements. The knowledge of the acoustical features of the facility used to perform such measurements is then one of the key points of such measurements. The proposed communication presents the recent results obtained in the test section of the Large Cavitation Tunnel (GTH at Val-de-Reuil) to describe the statistics of the diffuse acoustic field. The results show that the diffuse field complies spatially very well with the Gumbel distribution for narrow band levels (expressed in dB for the power spectral density). The limit of the statistical domain (defined as the “Schroeder frequency”) is also estimated thanks to the experimental measurements performed inside the test section.

Optimization approach for designing diffuse acoustic fields on demand

Optimization approach for designing diffuse acoustic fields on demand